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Q47.

Expert-verifiedFound in: Page 659

Book edition
Student Edition

Author(s)
Carter, Cuevas, Day, Holiday, Luchin

Pages
801 pages

ISBN
9780078884801

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

**10, 12, 15**

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

The length of the triangle is** **10, 12, 15** **

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

(i) If ${c}^{2}<{a}^{2}+{b}^{2}$, then the triangle is acute.

(ii) If ${c}^{2}={a}^{2}+{b}^{2}$, then the triangle is a right triangle.

(iii) If ${c}^{2}>{a}^{2}+{b}^{2}$, then the triangle is obtuse.

The triangle is having sides of measures 10, 12, and 15.

The longest side of the triangle is 15.

Therefore, the value *c* is 15.

Therefore, the values of *a* and *b* are 10 and 12 respectively.

Now, it can be obtained that:

$\begin{array}{c}{a}^{2}={10}^{2}=100\\ {b}^{2}={12}^{2}=144\\ {c}^{2}={15}^{2}=225\\ {a}^{2}+{b}^{2}=100+144=244\end{array}$

It can be noticed that:

$\begin{array}{c}{a}^{2}+{b}^{2}=244\\ {a}^{2}+{b}^{2}\ne {c}^{2}\end{array}$

As, ${c}^{2}\ne {a}^{2}+{b}^{2}$, 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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