Chapter 8, Problem 3CR

To determine

To find: the value of y.

Answer to Problem 3CR

The value of y is $5\sqrt{6}$

Explanation of Solution

Given Information: A triangle with a right angle and a perpendicular directed to the hypotenuse. The measure of sides is marked.

Formula used:

For a right triangle with a perpendicular being drawn to the hypotenuse (as shown below),the both small triangles are congruent to each other and to the bigger triangle. This gives the relation between the hypotenuse and the normal to it is expressed as,

  

  $\begin{array}{l}{b}^2=cx\\ b=\sqrt{cx}\end{array}$

Calculation:

Consider the triangle shown below.

  

For the given triangle, the one of the legs of the bigger triangle is represented by y and the parts of the hypotenuse considered is 10 and the total length of hypotenuse being 15. Thus, comparing with the general figure and formula, the value of y can be calculated as,

  $\begin{array}{c}y=\sqrt{10\times 15}\\ =\sqrt{150}\\ =5\sqrt{6}\end{array}$