Question

The difference between the sides at right angles in a right-angled triangle is 14cm. The area of the triangle is 120 square cm. Calculate the perimeter of the triangle.​

Answer 1

let one side at right angle be x

the other must be x-14

area of a triangle =(1/2) × (height) (base)

120 = (1/2)(x)(x-14)

120 = (x^2 -14x)/2

240 = x^2 -14x

x^2 -14x -240 = 0

x^2 -24x +10x -240 =0

x (x-24) + 10 (x-24) =0

(x-24)(x+10)=0

now, find x

x-24 =0

x = 24

again

x+10 =0

x = -10

as the side couldn't be -v so the value of x as a side must be 24cm

so the measure of one side we got is x =24cm and the other side = x-14 = 24 -14 =10cm

apply pythagoras theorem for third side as it is a right angled triangle

[let hypotaneous be a]

(24)^2 + (10^2) = a^2

576 +100 = a^2

676 = a^2

a = 26 cm

so the hypataneous = 26cm

perimeter of a triangle = sum of all sides

= (24 + 10 + 26 ) cm

= 60cm