Question

The triangles are similar. The area of the larger triangle is 800 cm².

What is the area of the smaller triangle?


12.5 cm²

50 cm²

100 cm²

200 cm²

Answer 1

The correct answer option is 50 cm
`^2`.

Explanation:

We are given two triangles that are similar with one of the corresponding sides with known values.

The ratio of the corresponding sides of the smaller triangle to the larger triangle is
`(16)/(64) =(1)/(4)`. So the ratio between the areas of these triangles will be
`(1)/(4^2) =(1)/(16)`.

If the area of the larger triangle is 800 cm
`^(2)` then the area of the smaller triangle will be =
`(1)/(16) *800=50`.

Therefore, the area of the smaller triangle is 50 cm
`^2`.

Answer 2

The area of the smaller triangle is
`50cm^2`

Explanation:

The given length of the bigger triangle is
`64cm`.

The length of the smaller triangle that corresponds to this side is
`16cm`.

We can see that the scale factor for this enlargement (reduction) is
`k=(1)/(4)`.

The scale factor for the area is
`k^2=(1)/(16)`.

Therefore to obtain the area of the smaller triangle, we need to multiply the area of the bigger triangle by
`(1)/(16)`.

This implies that,

`Area\:of\:smaller\:triangle=(1)/(16)* 800cm^2`

`Area\:of\:smaller\:triangle=50cm^2`

The correct answer is B