Question

The proportion between the hypotenuse of a right triangle and one of its legs is 13/12 , and the other leg is 15 cm long. Find the perimeter of the triangle.

Answer 1

The proportion between the hypotenuse of a right triangle and one of its legs is 13/12 , and the other leg is 15 cm long. Find the perimeter of the triangle.

Answer 2

The perimeter of the right angled triangle is 90 cm.

Let y represent the hypotenuse and x represent one of the legs. Hence:

y/x = 13/12

y = (13/12)x

Pythagoras theorem show the relationship between the sides of a right angled triangle. Hence:

y² = x² + 15²

[(13/12)x]² = x² + 225

169x²/144 = x² + 225

169x² = 144x² + 32400

25x² = 32400

x² = 1296

x = 36 cm

y = (13/12)x = (13/12)36 = 39 cm

Perimeter of triangle = x + y + 15 = 39 + 36 + 15 = 90 cm

Hence the perimeter of the right angled triangle is 90 cm.

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