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The figure shows a right-angled triangle, $ABC$ . $AB$ hypotenuese $= 7\,\text{cm}$ , $CD$ , a part of $CA = 3\,\text{cm}$ and $AD = BC$ . Find the area of triangle $ABC$ .

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Write and solve direct variation equations

Full solution

Q. The figure shows a right-angled triangle,

ABC

.

AB

hypotenuese

= 7\,\text{cm}

,

CD

, a part of

CA = 3\,\text{cm}

and

AD = BC

. Find the area of triangle

ABC

.

Find Side AC: Since ABC is a right-angled triangle, use Pythagoras theorem to find the length of side AC. $\newline$ $AC^2 = AB^2 - BC^2$ $\newline$ $AC^2 = 7^2 - 3^2$ $\newline$ $AC^2 = 49 - 9$ $\newline$ $AC^2 = 40$ $\newline$ $AC = \sqrt{40}$ $\newline$ $AC = 2\sqrt{10}$ cm
Calculate Area: Now, find the area of the triangle using the formula: Area = $(\text{base} \times \text{height}) / 2$ . Since $AD = BC$ and $CD$ is part of $CA$ , $AD = 3 \, \text{cm}$ . Area = $(AD \times BC) / 2$ Area = $(3 \times 3) / 2$ Area = $9 / 2$ Area = $4.5 \, \text{cm}^2$

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