# Can the numbers 24, 32, 40 be the lengths of the three sides of a right triangle?

In the right triangle, the square of the largest side should be equal to the sum of the square of the other two sides.

## Answer: Yes, the numbers 24, 32, 40 can be the lengths of the three sides of a right triangle.

Let's find out the answer step by step.

**Explanation: **

Given: 24, 32, 40 are the three sides of the right triangle

The right triangle formula state that the square of the hypotenuse of a triangle is equal to the sum of the square of the base and its altitude.

(Hypotenuse)^{2} = (Base)^{2} + (Altitude)^{2}

If these given lengths of a triangle satisfy the right triangle formula or Pythagorean theorem formula then they must be the sides of a right-angle triangle.

Let,

- The hypotenuse = 40 [Since the hypotenuse is the longest side]
- Base = 24.
- Altitude = 32.

Put these values in the Pythagorean formula,

(Hypotenuse)^{2} = (Base)^{2} + (Altitude)^{2}

40^{2} = 32^{2} + 24^{2}

⇒ 1600 = 1024 + 576

⇒ 1600 = 1600

Here,

L.H.S = R.H.S

We see that the given sides satisfy the Pythagorean theorem.

### Therefore, the numbers 24, 32, 40 can be the three sides of a right triangle.

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