Question

A right angled triangle has a hypotenuse of length 13 cm and a perimeter of length 30cm. find the length of the sides forming the right angle.​

Answer 1

Answer:

a=12

b=5

Step-by-step explanation:

Given,

c = 13cm

Perimeter, P = 30cm

We know,

Pythagoras theorem,

a² + b² = c² - - - - (1)

Perimeter of a triangle,

P = a + b + c - - - - (2)

where, a, b and c are the sides of the triangle.

30 = a + b + c

30 = a + b + 13

a + b = 17

Adding 2ab to both sides of the (1), we get

a² + b² + 2ab = c² + 2ab

(a + b)² = 13² + 2ab ( using (a+b)² = a² + 2ab + b²)

17² - 13² = 2ab

ab = (17² - 13²)/2 = 60

We have,

a + b = 17 => b = -a + 17

ab = 60 => a(-a + 17) + 60

-a² + 17a - 60 = 0

-a² + 17a - 60 = 0

a² - 17a + 60 = 0

using quadratic formula,

we have,

a = 5 or a = 12

b = -a + 17

=> b = -5 + 17 = 12

or

=> b = -12 + 17 = 5

Either a=5, b=12 or a=12, a=5

Check:

a² + b² = c²

LHS => 5² + 12² = 169 = 132 => RHS