Question

Both triangles are similar. The area of the smaller triangle is about 270 ft2. Which is the best approximation for the area of the larger triangle?

Answer 1

Both triangles are similar. The area of the smaller triangle is about 270 ft2. Which is the best approximation for the area of the larger triangle? small traingle side is 25ft the bigger traingle side is 35ft.

We know the relation between the area of similar triangles and the side length

`(Area(small))/(Area(big)l)` =
`(side_s^2)/(side_b^2)`

area of the smaller triangle= 270 ft2

Let the area of bigger triangle =x

small traingle side=25ft

the bigger triangle side = 35ft

Ratio of sides is 25 : 35 that is 5:7

Now we make a proportion

`(270)/(x)` =
`(5^2)/(7^2)`

270/x = 25/49

Cross multiply it

270 * 49 = 25 * x

13230 = 25x

divide by 25 on both sides

So x= 529.2

Area of larger triangle is approximately 530 square feet.