Chapter 11.2, Problem 35WE

To determine

To Find: The length of two diagonals if one is twice as long as others.

Answer to Problem 35WE

  $10and20$

Explanation of Solution

Given: The area of rhombus is $100$ .

Given: Area = $100$

Let the diagonal be $d_{1}and{d}_2$

Since

The length of two diagonals if one is twice as long as others.

Thus

  $d_1=2d_2$

Area of rhombus

  $\begin{array}{l}A=\frac{1}{2}{d}_1{d}_2\\ A=\frac{1}{2}(2d_2)(d_2)\\ $ 100={(d_2)}^2$d_2=10\\ now\\ d_1=2d_2\\ d_1=2(10)\\ d_1=20\end{array}$

Hence, the length of the diagonals are $10and20$ .