Question

(a) one triangle has side lengths 24, 25, and 7. compute the sum of the squares of the shorter lengths. ( 7^{2}+24^{2}=square ) compute the square of the longest length. ( 25^{2}=square ) what kind of triangle is it? acute triangle right triangle obtuse triangle (b) the other triangle has side lengths 7, 16, and 11. compute the sum of the squares of the shorter lengths. ( 7^{2}+11^{2}=square ) compute the square of the longest length. ( 16^{2}=square ) what kind of triangle is it? acute triangle right triangle obtuse triangle

Explanation:

Step1: Calculate \(7^{2}+24^{2}\)

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Step2: Calculate \(25^{2}\)

$$25^{2}=625$$

Since \(7^{2}+24^{2}=25^{2}\), it is a right - triangle.

Step3: Calculate \(7^{2}+11^{2}\)

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Step4: Calculate \(16^{2}\)

$$16^{2}=256$$

Since \(7^{2}+11^{2}=170<256 = 16^{2}\), by the rule \(a^{2}+b^{2}

Answer:

For part (a):
\(7^{2}+24^{2}=625\), \(25^{2}=625\), Right triangle.
For part (b):
\(7^{2}+11^{2}=170\), \(16^{2}=256\), Obtuse triangle.