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11
1 point
In the diagram a person who is
6ft tall is standing on the ground
3ft away from point
P. A line segment drawn from the top corner of the building to point
P creates two similar triangles.
Which proportion can be used to find
h, the height of the building in feet?

$11$ $\newline$ $1$ point $\newline$ In the diagram a person who is $6 \mathrm{ft}$ tall is standing on the ground $3 \mathrm{ft}$ away from point $P$ . A line segment drawn from the top corner of the building to point $P$ creates two similar triangles. $\newline$ Which proportion can be used to find $h$ , the height of the building in feet?

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Area of quadrilaterals and triangles: word problems

Full solution

Q.

11

\newline

1

point

\newline

In the diagram a person who is

6 \mathrm{ft}

tall is standing on the ground

3 \mathrm{ft}

away from point

P

. A line segment drawn from the top corner of the building to point

P

creates two similar triangles.

\newline

Which proportion can be used to find

h

, the height of the building in feet?

Identify Similar Triangles: Identify the similar triangles in the diagram. The person and the building form two similar triangles with point $P$ .
Set Up Proportion: Set up the proportion using the corresponding sides of the similar triangles. Let $x$ be the height of the building. The person's height ( $6$ ft) is to their distance from point $P$ ( $3$ ft) as the building's height ( $x$ ) is to the distance from the building to point $P$ (which is also $3$ ft since the person is standing right at point $P$ ). $\newline$ So, the proportion is $\frac{6}{3} = \frac{x}{3}$ .
Solve Proportion: Solve the proportion for $x$ . Cross-multiply to get $6 \times 3 = x \times 3$ .
Simplify Equation: Simplify the equation. $18 = 3x$ .
Calculate x Value: Divide both sides by $3$ to solve for x. $x = \frac{18}{3}$ .
Calculate x Value: Divide both sides by $3$ to solve for x. $x = \frac{18}{3}$ .Calculate the value of x. $x = 6$ .

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\newline

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