Question

(b) The other triangle has side lengths 12, 8, and 11.

Compute the sum of the squares of the shorter lengths
8² + 11² = 0
Compute the square of the longest length.
12² = 0-
What kind of triangle is it?
Acute triangle
ORight triangle
Obtuse triangle

Answer 1

Sum of shorter lengths' squares = 185

Square of longest length = 144

Type of triangle = acute

Explanation:

(b) Part 1:

As it's written, the shortest sides are 8 and 11 units long, so now we can find the sum of their squares:

8^2 + 11^2

64 + 121

185

Thus, the sum of the squares of the shorter lengths is 185.

(b) Part 2:

We're also told that the longest side is 12 units long, so now we can find its square:

12^2

144

Thus, the square of the longest side is 144.

(b) Part 3:

We can let a, b, and c represent the three side length, where

• a and b are the shorter sides (the particular order doesn't matter so we can let a = 8 and b = 11),
• and c is the longest side (i.e., 12 in this case).

The squares of a triangle's side lengths can help us determine the triangle's type as it reveals one of three things:

• If c^2 < a^2 + b^2, we have an acute triangle
• If c^2 = a^2 + b^2, we have a right triangle.
• If c^2 > a^2 + b^2, we have an obtuse triangle.

Now we can determine which type of triangle we have:

• We know that a^2 + b^2 for this problem is 185 while c^2 is 144.

Since 144 < 185, we have an acute triangle.