Chapter 8, Problem 13CT

To determine

To find: the values of x

Answer to Problem 13CT

The value of x is $11\sqrt{2}$ .

Explanation of Solution

Given Information: A square with length of side 11 units and with a diagonal of unknown measure.

Formula used:

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 figure given below.

  

In the given square, each of the angles are right angles. So, two isosceles right triangles are formed by the sides and diagonal as in the figure. Now, the diagonal of the square represents the hypotenuse of the triangle.

The length of hypotenuse can be calculated using the Pythagoras theorem as,

  $\begin{array}{c}x=\sqrt{{11}^2+{11}^2}\\ =11\sqrt{2}\end{array}$