#### 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.

#### Solution

Let the length of one side of right triangle be = x cm then other side be = (x + 5) cm

And given that hypotenuse = 25 cm

As we know that by Pythagoras theorem,

x^{2} + (x + 5)^{2} = (25)^{2}

x^{2} + x^{2} + 10x + 25 = 625

2x^{2} +10x + 25 - 625 = 0

2x^{2} + 10x - 600 = 0

x^{2} + 5x - 600 = 0

x^{2} - 15x + 20x - 600 = 0

x(x - 15) + 20(x - 15) = 0

(x - 15)(x + 20) = 0

So, either

x - 15 = 0

x = 15

Or

x + 20 = 0

x = -20

But the side of right triangle can never be negative

Therefore, when x = 15 then

x + 5 = 15 + 5 = 20

Hence, length of one side of right triangle be 15 cm then other side be 20 cm.

Is there an error in this question or solution?

#### APPEARS IN

Solution 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. Concept: Solutions of Quadratic Equations by Factorization.