Chapter 11.7, Problem 15WE

To determine

To Find: The area of similar quadrilateral whose longest side is $15cm$ .

Answer to Problem 15WE

  $125c{m}^2$

Explanation of Solution

Given: A quadrilateral with sides $8cm,9cm,6cm,5cm$ has area $45c{m}^2$ .

Since two quadrilaterals are equal.

Thus

The longest side of the two quadrilaterals is a pair of corresponding sides.

So

Longest side of first quadrilateral is $9cm$ and second one is $15cm$ .

Thus the scale factor is

  $9:15$

For two similar triangles ratio of area is $a^2:b^2$ .

  $\begin{array}{l}{a}^2:b^2=9^2:{15}^2\\ =81:225\end{array}$

Now

Let the area of second quadrilateral is $x$ .

Area of first quadrilateral is $45c{m}^2$ .

Thus

  $\begin{array}{l}\frac{45}{x}=\frac{81}{225}\\ x=125c{m}^2\end{array}$

Hence,

The area of second quadrilateral is $125c{m}^2$ .