Question

The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.

Answer 1

SOLUTION :  

Given : Hypotenuse of a right triangle = 25 cm

Let the length of one side be x cm and the other side be (x + 5)cm

By Pythagoras theorem :  

H² = B² + P²

(25)² = x² + (x + 5)²

625 = x² + x² + 5² + 2×x×5

[(a + b)² = a² + b² + 2ab]

625 = 2x² + 10x + 25

2x² + 10x + 25 - 625 = 0

2x² + 10x – 600 = 0

2(x² + 5x – 300) = 0

x² + 5x – 300 = 0

x² + 20x – 15x – 300 = 0

[By middle term splitting]

x(x + 20) –15(x + 20) = 0

(x + 20) (x –15) = 0

(x + 20) or (x –15) = 0

x = - 20 or  x = 15

since, length of side can't be negative ,so x ≠ - 20 . Therefore , x = 15  

one side = x = 15 cm

other side = (x + 5) = 15 + 5 = 20 cm

Hence, the length of two sides of the ∆ are 15 cm &  20 cm.

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Answer 2

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