Question

The difference of lengths of side forming right angled triangle is 3 cm. If the perimeter of the triangle is 36 cm.Find the area of the triangle​

Answer 1

Let the perpendicular height be x

Let the base of triangle be x + 3

by Pythagoras theorem

hypotenuse = x² + (x + 3)²

hypotenuse = 2x² + 6x + 9

As the perimeter of the triangle is 36 cm

36 = 2x² + 6x + 9 + x + x + 3

36 = 2x² + 8x + 12

2x² + 8x - 24 = 0

x² + 4x - 12

x(x + 6) - 2(x + 6) = 0

(x - 2) (x + 6) = 0

x = 2, -6

rejecting -6

x = 2 cm

The perpendicular = 2 cm

The base = 5 cm

Answer 2

Answer:

base=5

perpendicular=2