Chapter 8, Problem 25CT

To determine

The length of diagonal of the rhombus.

Answer to Problem 25CT

Length of the other diagonal of the rhombus is $4\sqrt{3}$ .

Explanation of Solution

Given information:

The length of diagonal is 4 units and sides are of 4 units of a rhombus.

Let x be the length of half of the other diagonal of the rhombus

Diagonal of a rhombus cuts each other at right angle and forms a right angle triangle

So the side of rhombus will be the hypotenuse of the right angle triangle

Half of the length of the given diagonal will be 2 units

By the Pythagoras theorem

  $\begin{array}{c}{\left(hypo.\right)}^2={\left(perp.\right)}^2+{\left(base\right)}^{{}^2}\\ 4^2=2^2+x^2\\ x^2=16-4\\ x=\sqrt{12}\\ x=2\sqrt{3}\end{array}$

So the length of the other diagonal is $2x=4\sqrt{3}$