Chapter 11.2, Problem 17WE

To determine

To Find: The area.

Answer to Problem 17WE

  $A=240sq.unit$

Explanation of Solution

Given: A rhombus with perimeter $68$ and one diagonal $30$ .

  

Perimeter: $68$

i.e.

  $\begin{array}{l}68=4a\\ a=17\end{array}$

Now

One diagonal is $30$ .

Diagonals of a rhombus bisect each other.

Now in triangle $AOC$

  $\begin{array}{l}{17}^2=x^2+{15}^2\\ x^2={17}^2-{15}^2\\ x=8\end{array}$

Area of rhombus

  $\begin{array}{l}A=\frac{d_1{d}_2}{2}\\ A=\frac{30\cdot 16}{2}\\ A=240sq.unit\end{array}$

Hence, $A=240sq.unit$