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Chapter 3: Q. 399 (page 408)

In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse.

Short Answer

Expert verified

The length of the hypotenuse is26.

Step by step solution

01

Step 1. Given Information

We are given a right angled triangle whose lengths of two legs are 24and 10.

We need to find the length of the hypotenuse of the triangle.

02

Step 2. Concept used

The Pythagorean Theorem states that in any right triangle, a2+b2=c2where cis the length of the hypotenuse and aand bare the lengths of the legs.

03

Step 3. Find the hypotenuse

As the two legs are of length 24and 10. So in the equation a2+b2=c2substitute 24for aand 10for b.

242+102=c2576+100=c2676=c2

Taking square root both sides we get

676=c226=c

So the length of the hypotenuse is 26.

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