Chapter 8, Problem 14CUR

To determine

To calculate: the length of one side of a rhombus for a given length of diagonals.

Answer to Problem 14CUR

The length of one side of the rhombus is $15$

Explanation of Solution

Given Information: The diagonals of a rhombus are of the measure 18 and 24.

Formula used:

1) The diagonals of a rhombus bisect each other at right angles.

2) The relationship between the legs of right triangle (shown in figure below) a , b and its hypotenuse c is obtained by using Pythagoras theorem.

  

It can be expressed as,

  $\begin{array}{l}{c}^2=a^2+b^2\\ c=\sqrt{a^2+b^2}\end{array}$

Calculation: Consider the rhombus given below.

  

Since, the diagonals are perpendicular to each other and bisect at their point of intersection, the triangle OEF, and the remaining three triangles are right angled triangles. Here, the side of the rhombus acts as the hypotenuse of the triangles. The sides of a rhombus are equal. Hence, the length of a side can be expressed using the Pythagoras theorem as,

  $\begin{array}{c}{a}^2=\sqrt{9^2+{12}^2}\\ a=\sqrt{81+144}\\ =\sqrt{225}\\ =15\end{array}$