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In a right - angled triangle, the hypotenuse is 4 cm longer than the perpendicular which is 4 cm longer than the base. Calculate the length of the hypotenuse. A. 12 cm B. 10 cm C. 20 cm D. 15 cm

In a right - angled triangle, the hypotenuse is 4 cm longer than the perpendicular which is 4 cm longer than the base. Calculate the length of the hypotenuse. A. 12 cm B. 10 cm C. 20 cm D. 15 cm Correct Answer C

Let base of the triangle be x cm

Perpendicular of the triangle = x + 4

Hypotenuse of the triangle = x + 4 + 4 = x + 8

As we know,

(Hypotenuse)2 = (Base)2 + (Perpendicular)2

(x + 8)2 = x2 + (x + 4)2

⇒ x2 + 64 + 16x = x2 + x2 + 16 + 8x

⇒ x2 – 8x – 48 = 0

⇒ x2 – 12x + 4x – 48 = 0

⇒ x(x – 12) + 4(x – 12) = 0

⇒ (x – 12)(x + 4) = 0

Taking,

⇒ x – 12 = 0

⇒ x = 12

Length of the hypotenuse = 12 + 8 = 20 cm

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