Question

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Answer 1

Since the triangles are similar, the ratio of the sides of larger triangle to the smaller triangle is a constant.

That constant = $\frac{15}{9} = \frac{5}{3}$

Since the sides are in that constant proportion, the area of the triangles will also be in proportion.

(Area of larger triangle) over (Area of smaller triangle) = $\frac{5}{3}$

$\frac{206}{x} = \frac{5}{3}$

$x = 206 * \frac{3}{5} = \frac{618}{5}$ = 123.6 ≈ 124

Hence, to the nearest whole number the area of smaller triangle is 124 ft².

Answer 2

Answer:

Area of the smaller triangle 74  ft².

Step-by-step explanation:

Given  : The triangles are similar. The area of the larger triangle is 206 ft^2.

To find : Find the area of the smaller triangle to the nearest whole number.

Solution : We have given that triangles are similar and area of the larger triangle is 206 ft^2.

By the similar triangles property : $\frac{Area\ of\ triangle 1}{Area\ of\ triangle\ 2} = \frac{(side\ of\ triangle\ 1)^{2}}{(side\ of\ triangle\ 2)^{2} }$.

Then Side of triangle 1 = 15 ft .

Side of triangle 2 = 9 ft.

Area of triangle 1 = 206 ft².

Let area of triangle 2 = x.

Then ,

Ratio of sides = $\frac{15}{9}$ =  $\frac{5}{3}$

$\frac{206}{x} = \frac{(5)^{2}}{(3)^{2} }$.

$\frac{206}{x} = \frac{(25}{9}$.

On cross multiplication :

206 * 9 = 25  *x

1854 = 25 * x .

On dividing by 25

x = 74.16 ft².

Therefore, Area of the smaller triangle 74  ft².