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the triangles are similar. the area of the larger triangle is 206 ft^2. find the area of the smaller triangle to the nearest whole number.

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 : .

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 = =  

.

.

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.

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