Question

one triangle has side lengths 19, 13, and 17. (a) compute the sum of the squares of the shorter lengths. 13² + 17² = □ compute the square of the longest length. 19² = □ what kind of triangle is it? acute triangle right triangle obtuse triangle the other triangle has side lengths 12, 15, and 9. (b) compute the sum of the squares of the shorter lengths. 9² + 12² = □ compute the square of the longest length. 15² = □ what kind of triangle is it? acute triangle right triangle obtuse triangle

Explanation:

Step1: Calculate sum of squares of shorter sides for (a)

$13^{2}+17^{2}=169 + 289=458$

Step2: Calculate square of longest side for (a)

$19^{2}=361$

Step3: Compare for (a)

Since $13^{2}+17^{2}>19^{2}$, it is an acute - triangle.

Step4: Calculate sum of squares of shorter sides for (b)

$9^{2}+12^{2}=81 + 144 = 225$

Step5: Calculate square of longest side for (b)

$15^{2}=225$

Step6: Compare for (b)

Since $9^{2}+12^{2}=15^{2}$, it is a right - triangle.

Answer:

(a)
Compute the sum of the squares of the shorter lengths: $458$
Compute the square of the longest length: $361$
What kind of triangle is it? Acute triangle
(b)
Compute the sum of the squares of the shorter lengths: $225$
Compute the square of the longest length: $225$
What kind of triangle is it? Right triangle