Question

The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the lengths of other two sides of the triangle.

Answer 1

Given:

Perimeter of the right triangle = 60 cm

Hypotenuse (c) = 25 cm

Let the other two sides be a and b.

The perimeter of a triangle is given by,

a + b + c = 60

Substituting c = 25

a + b + 25 = 60

a + b = 35     ...(1)

In a right-angled triangle 

a² + b² = c²    ...[Using Pythagoras theorem]

Substituting c = 25

a² + b² = 25²

a² + b² = 625    ...(2)

b = 35 − a    ...[From  equation (1)]

Substituting this value of b in equation (2), we get

a² + (35 − a)² = 625

∴ a² + (1225 − 70a + a²) = 625

∴ 2a² − 70a + 1225 = 625

∴ 2a² − 70a + 600 = 0    ...(3)

Divide equation (3) by 2, we get

a² − 35a + 300 = 0

Using the quadratic formula, where 

a = `(-(-35) +- sqrt((-35)^2 - 4(1)(300)))/(2(1))`

∴ a = `(35 +- sqrt(1225 - 1200))/2`

∴ a = `(35 +- sqrt 25)/2`

∴ a = `(35 +- 5)/2`

∴ a = `(35 + 5)/2`

∴ a = `40/2`

∴ a = 20

OR

a = `(35 - 5)/2`

∴ a = `30/2`

∴ a = 15

Thus, the possible values are (a, b) = (20, 15) or (15, 20)

∴ The lengths of the other two sides are 15 cm and 20 cm.