Chapter 9, Problem 33RP

To determine

To find:The ratio of legs in a right triangle.

Answer to Problem 33RP

The ratio of legs in a right triangle is 1: 4

Explanation of Solution

Given information:

The altitude to the hypotenuse of a right triangle divides the hypotenuse in the ratio 4 : 1

Formula used:

Ratio of corresponding sides of similar triangles are equivalent

Calculation :

In triangles ABC and ABD, we have

  

  $\begin{array}{l}AB=AB\mathrm{.....}\text{common arm}\\ \angle ADB=\angle ABC=90°\\ \angle BAD=\angle BAC\mathrm{......}\text{common angle}\\ \angle BDA=\angle BCA\\ \therefore \Delta ABC\sim ABD\\ \text{Hence,}\\ \frac{AB}{BC}=\frac{AD}{CD}=\frac{1}{4}\mathrm{......}\because \text{given},\frac{CD}{AD}=\frac{4}{1}\end{array}$

Thus,

Required ratio = 1: 4