Question

(a) one triangle has side lengths 5, 11, and 7.
compute the sum of the squares of the shorter lengths.
$5^{2}+7^{2}=\square$
compute the square of the longest length.
$11^{2}=\square$
what kind of triangle is it?
acute triangle
right triangle
obtuse triangle

(b) the other triangle has side lengths 14, 13, and 9.
compute the sum of the squares of the shorter lengths.
$9^{2}+13^{2}=\square$
compute the square of the longest length.
$14^{2}=\square$
what kind of triangle is it?
acute triangle
right triangle
obtuse triangle

Explanation:

Step1: Calculate \(5^{2}+7^{2}\)

$$
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$$

Step2: Calculate \(11^{2}\)

$$ 11^{2}=121 $$

Since \(74<121\), for triangle with sides \(5\), \(7\), \(11\), it is an obtuse triangle (because if \(a^{2}+b^{2}

Step3: Calculate \(9^{2}+13^{2}\)

$$
LATEXBLOCK1
$$

Step4: Calculate \(14^{2}\)

$$ 14^{2}=196 $$

Since \(250>196\), for triangle with sides \(9\), \(13\), \(14\), it is an acute triangle (because if \(a^{2}+b^{2}>c^{2}\) where \(c\) is the longest side, the triangle is acute)

Answer:

(a) \(5^{2}+7^{2}=74\), \(11^{2} = 121\), Obtuse triangle.
(b) \(9^{2}+13^{2}=250\), \(14^{2}=196\), Acute triangle.