Question

The difference between the sides at right angles in a right angled triangle is 7 cm the area of the triangle is 60 cm find its perimeter

Answer 1

Answer:

Step-by-step explanation:

Area of right angled triangle = ½ (base * height)

=  = ½ (Base × Perpendicular)

Let base be b then perpendicular = b+7

So ½ (b) (b+7) = 60

b² + 7b - 120 = 0

b² + 15b - 8b - 120 = 0

b(b+15) - 8(b+15) = 0

(b-8)(b+15) = 0

b = 8 or -15

Side cannot be negative so base = 8

Perpendicular = 15

By Pythagoras theorem:

Hypotenuse = √8² + 15²

Hypotenuse = √64+225 = √289 = 17

Hence Perimeter = 8+15+17 = 40 cm