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 in a right angle be x cm and `(x-14).` cm
then , its area `=[(1)/(2)xx x xx(x-14)]cm^(2)`.
But area `=120 cm^(2) ["given"].`
`therefore (1)/(2) x(x-14)=120 implies x^(2)-14x-240 =0`
`implies x^(2)-24 x+10x-240=0implies x(x-24)+10(x-24)=0`
`implies(x-24)(x+10)=0impliesx=24["neglecting "x=-10].`
`therefore "one side "=24cm ,and "other side " =(24-14) cm =10 cm.`
Hypotenuse `=sqrt((24)^(2)+(10)^(2))cm =sqrt(576+100)cm `
` =sqrt(676) cm = 36 cm.`
`therefore ` Perimeter of the triangle `=(24+10+26) cm =60cm`.