Question

The hypotenuse of a right angled triangle is 13 cm. and the difference of the other two sides is 7 cm. Find the perimeter of the triangle
​

Answer 1

Answer:

30 cm

Step-by-step explanation:

We have,

Hypotenuse of a right angled triangle = 13 cm.

Let the length of the first side be 'x' cm.

Given that difference between the other two sides is 7 cm.

⇒ x² + (x + 7)² = 13²

⇒ x² + x² + 49 + 14x = 169

⇒ 2x² + 14x - 120 = 0

⇒ x² + 7x - 60 = 0

⇒ x² + 12x - 5x - 60 = 0

⇒ x(x + 12) - 5(x + 12) = 0

⇒ (x - 5)(x + 12) = 0

⇒ x = 5.

Then:

x + 7 = 12 cm.

∴ Perimeter of the triangle = 30 cm

Hope it helps!

Answer 2

x² + (x + 7)² = 13²

⇒ x² + x² + 49 + 14x = 169

⇒ 2x² + 14x - 120 = 0

⇒ x² + 7x - 60 = 0

⇒ x² + 12x - 5x - 60 = 0

⇒ x(x + 12) - 5(x + 12) = 0

⇒ (x - 5)(x + 12) = 0

⇒ x = 5.

Then:

x + 7 = 12 cm.

∴ Perimeter of the triangle = 30 cm