Question

Find the values of x and y when the smaller triangle has an area of 45 cm².
PLS PLS PLS HELP

Answer 1

Given two similar triangles

The corresponding sides are proportions

So,

`(x)/(y) =(20)/(90) =(2)/(9)`

So, the relation between x and y will be:

`x=(2)/(9) y`

The area of the smaller triangle = 45 cm²

So, area =

`(1)/(2) x* y=45`

Substitute with x into the equation of the area to find the value of y

`(1)/(2) *(2)/(9) y* y=45`

`y^2=(45*1*9)/(2) =(405)/(2)=202.5`

`y=√(202.5)`

Substitute with y into x

`x=(2)/(9) *√(202.5) =(2√(202.5) )/(9)`

So, the answer will be:

`x=(2√(202.5) )/(9)`

`y=√(202.5)`