# Two sides of a right triangle, the adjacent and hypotenuse, are 3x and 5x, the perimeter is 84, find x?

##### 1 Answer

Jun 2, 2016

x = 7

#### Explanation:

The perimeter = sum of all 3 sides of the triangle. We are given 2 and therefore require to find the 3rd side.

Since the triangle is right with the hypotenuse = 5x , use

#color(blue)"Pythagoras' theorem"# to find 3rd side which we can name h , say.

#rArr(5x)^2=(3x)^2+h^2# hence

#h^2=(5x)^2-(3x)^2=25x^2-9x^2=16x^2# now

#h^2=16x^2rArrh=sqrt(16x^2)=4x# perimeter = 5x + 3x + 4x = 84

thus : 12x = 84 → x = 7