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Determine whether each set of measures can be the lengths of the sides of a right triangle.

12, 16, 21

Short Answer

Expert verified

The given set of measures is not the lengths of the sides of a right triangle.

Step by step solution

01

Step1. Given 

The length of the triangle is12,16,2112,16,21

02

Step2. Determine how to identify whether the given measures are the sides of the right triangle, acute triangle, an obtuse triangle.

If,c is the longest side of the triangle,a andb are the other two sides of the triangle then:

(i) If c2<a2+b2, then the triangle is acute.

(ii) If c2=a2+b2, then the triangle is a right triangle.

(iii) If c2>a2+b2, then the triangle is obtuse.

03

Step3. Determine whether the given set of measures can be the lengths of the sides of a right triangle.

The triangle is having sides of measures 12, 16, and 21.

The longest side of the triangle is 21.

Therefore, thec value is 21.

Therefore, the values ofa andb are 12 and 16 respectively.

Now, it can be obtained that:

a2=122=144b2=162=256c2=212=441a2+b2=144+256=400

It can be noticed that:

role="math" localid="1648101896700" a2+b2=400a2+b2c2

As, c2a2+b2, therefore, the triangle is not a right triangle.

Therefore, the given set of measures is not the lengths of the sides of a right triangle.

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