# The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

**Solution:**

In a right triangle, altitude is one of the sides.

Let the base be x cm.

The altitude will be (x - 7) cm.

We can now apply the Pythagoras theorem to the given right triangle.

Pythagoras theorem: Hypotenuse^{2} = (side 1)^{2} + (side 2)^{2}

13^{2} = x^{2} + (x - 7)^{2}

13^{2} = x^{2} + (x - 7)^{2}

169 = x^{2} + x^{2} - 14x + 49

169 = 2x^{2} - 14x + 49

2x^{2} - 14x + 49 -169 = 0

2x^{2} - 14x - 120 = 0

(2x^{2} - 14x - 120) / 2 = 0

x^{2} - 7x - 60 = 0

x^{2} - 12x + 5x - 60 = 0

x(x - 12) + 5 (x - 12) = 0

(x + 5) (x - 12) = 0

x - 12 = 0 and x + 5 = 0

x = 12 and x = - 5

We know that the value of the base cannot be negative.

Therefore, Base = 12 cm, Altitude = 12 - 7 = 5 cm

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 4

**Video Solution:**

## The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides

Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.2 Question 5

**Summary:**

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm then the other two sides are 12 cm and 5 cm.

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