Answer:
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.