The difference between the sides at right angles in a right - angled triangle is 14 cm . The area of the trangle is `120 cm^(2)` . Calculate the perimeter of the triangle.

Explanation

Let the sides containing the right angle be x cm and (x - 14)cm.
Then, the area of the triangle `=[(1)/(2) xx x xx (x-14)]cm^(2)`.
But, area = 120 `cm^(2)` (given).
`therefore" "(1)/(2)x(x-14)=120`
`rArr" "x^(2)-14x - 240 = 0` `rArr" "x^(2)-24x + 10x - 240`
`rArr" "x(x-24)+10(x-24)`
`rArr" "(x-24)(x+10)=0`
`rArr" "x = 24` (neglecting x = -10).
`therefore" "`one side = 24 cm, other side = (24 - 10) cm = 10 cm.
Hypotenuse `=sqrt((24)^(2)+(10)^(2))cm=sqrt(576+100)cm`
`=sqrt(676)cm = 26 cm`.
`therefore" "` perimeter of the triangle = ( 24 + 10 + 26) cm = 60 cm.