Chapter 11.2, Problem 18PPS

To determine

To find: The missing length.

Answer to Problem 18PPS

The two diagonals are of $31.0\text{in}$ and $15.5\text{in}$ .

Explanation of Solution

Given:

The diagonal of the kite is twice as long as the other diagonal.

The area of the kite is $240{\text{in}}^2$ ,

Calculation:

Consider the diagonal of the kite is twice as long as the other diagonal then,

  $d_1=2d_2$

Then, the area of the kite is obtained as,

  $\begin{array}{l}A=\frac{d_1{d}_2}{2}\\ 240{\text{in}}^2=\frac{2d_2{d}_2}{2}\\ d_2^2=240{\text{in}}^2\\ d_2=15.5\text{in}\end{array}$

Then, the other diagonal is obtained as,

  $\begin{array}{c}{d}_1=2\left(15.5\text{in}\right)\\ =31.0\text{in}\end{array}$

Thus, the two diagonals are of $31.0\text{in}$ and $15.5\text{in}$ .