Solve For Missing Dimension Of A Triangle Given Area Problems

<p>A triangle has an area of `120` `text{cm}^2`. </p><p>What is the base (`b` cm) of the triangle?<highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal. </highlight></p><UiTriangleV2 data-props='{ "options": { "cell_size": 16, "rows": 8, "columns": 15, "padding": 1, "xOffset": -4, "yOffset": 0 }, "scale_factor": 8, "vertex": { "top": { "angle": 91.9 }, "left": { "angle": 59 }, "right": { "angle": 29.1 } }, "sides": { "base": { "label": { "label": "b" } }, "left": { "label": { "label": "" } }, "right": {}, "altitude": { "label": { "label": "10 cm", "labelXOffset": 50 } } }, "arcs": [ { "position": "altitude", "show_arc": true } ], "background_color": "white", "border_color": "black", "area": { "text": "120 cm", "position": "top", "color": "black" }}'></UiTriangleV2 >

<p>A triangle has an area of `56` `text{in}^2`. </p><p>What is the height (`h` in) of the triangle?<highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal. </highlight></p><UiTriangleV2 data-props='{ "options": { "cell_size": 16, "rows": 8, "columns": 15, "padding": 1, "xOffset": 2, "yOffset": 0 }, "scale_factor": 6.5, "vertex": { "top": { "angle": 80.4 }, "left": { "angle": 41.6 }, "right": { "angle": 58 } }, "sides": { "base": { "label": { "label": "14 in" } }, "left": { "label": { "label": "12 in" } }, "right": {}, "altitude": { "label": { "label": "h" } } }, "arcs": [ { "position": "altitude", "show_arc": true } ], "background_color": "white", "border_color": "black", "area": { "text": "56 in", "position": "top", "color": "black" }}'></UiTriangleV2 >

<p>A triangle has an area of `70` `text{cm}^2`. </p><p>What is the height (`h` cm) of the triangle?<highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal. </highlight></p><UiTriangleV2 data-props='{ "options": { "cell_size": 15, "rows": 12, "columns": 16, "padding": 1, "xOffset": -0.5, "yOffset": 0 }, "scale_factor": 7, "vertex": { "top": { "angle": 69.6 }, "left": { "angle": 56.9 }, "right": { "angle": 53.5 } }, "sides": { "base": { "label": { "label": "14 cm" } }, "left": { "label": { "label": "12 cm" } }, "right": {}, "altitude": { "label": { "label": "h" } } }, "arcs": [ { "position": "altitude", "show_arc": true } ], "background_color": "white", "border_color": "black", "area": { "text": "70 cm", "position": "top", "color": "black" }}'></UiTriangleV2 >

<p>A triangle has an area of `96` `text{mm}^2` .</p><p>What is the height (`h` mm) of the triangle?<highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal. </highlight></p><UiTriangleV2 data-props='{ "options": { "cell_size": 16, "rows": 9, "columns": 15, "padding": 1, "xOffset": 1 }, "scale_factor": 10, "vertex": { "top": { "angle": 27.1 }, "left": { "angle": 127.7 }, "right": { "angle": 25.2 } }, "sides": { "base": { "label": { "label": "16 mm" } }, "left": { "label": { "label": "15 mm" , "labelYOffset": 2, "labelXOffset": 10 } }, "right": {}, "altitude": { "label": { "label": "h" } } }, "arcs": [ { "position": "altitude", "show_arc": true } ], "background_color": "white", "border_color": "black", "area": { "text": "96 mm", "position": "top", "color": "black" }}'></UiTriangleV2 >

<p>A triangle has an area of `81` `text{in}^2` .</p><p>What is the height (`h` in) of the triangle?<highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal. </highlight></p><UiTriangleV2 data-props='{ "options": { "cell_size": 15, "rows": 8, "columns": 16, "padding": 1, "xOffset": 0.5, "yOffset": 1 }, "scale_factor": 10, "rotation_angle": 0, "disableLabelRotation": true, "vertex": { "top": { "angle": 30.2 }, "left": { "angle": 130.2 }, "right": { "angle": 19.6 } }, "sides": { "base": { "label": { "label": "18 in" } }, "left": { "label": { "label": "12 in", "labelXOffset": 8,"labelYOffset": 1 } }, "right": {}, "altitude": { "label": { "label": "h" } } }, "arcs": [ { "position": "altitude", "show_arc": true } ], "background_color": "white", "border_color": "black", "area": { "text": "81 in", "position": "top", "color": "black" }}'></UiTriangleV2 >

<p> The triangle has an area of `34.5` `text{mm}^2`. </p> <p>What is the base (`b` mm) of the triangle?<highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal. </highlight></p><UiTriangleV2 data-props='{ "options": { "cell_size": 16, "rows": 8, "columns": 15, "padding": 1, "xOffset": 1.5, "yOffset": 1 }, "scale_factor": 8.5, "rotation_angle": 0, "disableLabelRotation": true, "vertex": { "top": { "angle": 37.1 }, "left": { "angle": 121.2 }, "right": { "angle": 21.7 } }, "sides": { "base": { "label": { "label": "b" }, "color": "black" }, "left": { "label": { "label": "7 mm", "labelXOffset": 8, "labelYOffset": 1 }, "color": "black" }, "right": { "label": { "label": "16.3 mm" }, "color": "black" }, "altitude": { "label": { "label": "6 mm","labelXOffset":-6 }, "color": "black" } }, "arcs": [ { "position": "altitude", "show_arc": true } ], "background_color": "white", "border_color": "black", "area": { "text": "34.5 mm", "position": "top", "color": "" }}'></UiTriangleV2 >

<p> The triangle has an area of `13.5` `text{cm}^2`. </p><p>What is the height (`h` cm) of the triangle?<highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal. </highlight><UiTriangleV2 data-props='{ "options": { "cell_size": 16, "rows": 15, "columns": 13, "padding": 1, "xOffset": -2.5, "yOffset": 1.5 }, "scale_factor": 7, "rotation_angle": 0, "disableLabelRotation": true, "vertex": { "top": { "angle": 66.5 }, "left": { "angle": 63.7 }, "right": { "angle": 49.8 } }, "sides": { "base": { "label": { "label": "6 cm" } }, "left": { "label": { "label": "5 cm", "label_color": "black" } }, "right": { "label": { "label": "5.9 cm", "labelXOffset": -3, "label_color": "black", "labelYOffset": -1 } }, "altitude": { "label": { "label": "h", "labelYOffset": 5, "labelXOffset": 5, "label_color": "black" }, "color": "black", "right": true } }, "arcs": [ { "position": "altitude", "color": "", "show_arc": true } ], "background_color": "white", "border_color": "black", "rotation_angle": -90, "area": { "text": "13.5 cm", "position": "top" }, "disableLabelRotation": false}'></UiTriangleV2 >

<p> The triangle has an area of `31.5` `text{cm}^2`. </p> <p>What is the base (`b` cm) of the triangle?<highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal. </highlight></p><UiTriangleV2 data-props='{ "options": { "cell_size": 16, "rows": 15, "columns": 11, "padding": 1, "xOffset": -5.5, "yOffset": 3 }, "scale_factor": 7, "rotation_angle": 0, "disableLabelRotation": true, "vertex": { "top": { "angle": 75.9 }, "left": { "angle": 67.3 }, "right": { "angle": 36.8 } }, "sides": { "base": { "label": { "label": "b", "label_color": "black", "labelXOffset": 0 }, "color": "black" }, "left": { "label": { "label": "6.5 cm","labelXOffset":1.5 } }, "right": { "label": { "label": "10 cm", "labelXOffset": -5 } }, "altitude": { "label": { "label": "6 cm", "label_color": "black" ,"labelXOffset":3,"labelYOffset":5}, "right": true, "color": "black" } }, "arcs": [ { "position": "altitude", "show_arc": true } ], "background_color": "white", "border_color": "black", "rotation_angle": -90, "area": { "text": "31.5 cm", "position": "top", "color": "" }, "disableLabelRotation": false}'></UiTriangleV2 >