Chapter 8, Problem 7CT

To determine

To find: the values of x and y

Answer to Problem 7CT

The value of x and y is $\sqrt{13},2\sqrt{3}$ respectively.

Explanation of Solution

Given Information:

Two right triangles with same hypotenuse with measures of two sides of one of the triangles being given in the figure.

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 ΔABC, $\angle B$ forms the right angle and the length of the hypotenuse is denoted by the variable x. It can be calculated by the Pythagoras theorem as,

  $\begin{array}{c}x=\sqrt{2^2+3^2}\\ =\sqrt{13}\end{array}$

Similarly, the value of y can be calculated by the Pythagoras theorem in ΔADC as,

  $\begin{array}{c}x=\sqrt{1^2+y^2}\\ \sqrt{13}=\sqrt{1^2+y^2}\end{array}$

The equation can be rearranged to find the value of y as follows.

  $\begin{array}{c}{y}^2=13-1\\ =12\\ y=\sqrt{12}\\ =2\sqrt{3}\end{array}$