Question by Photo:
Answer:
1. Length of AB: This can be found by using the Pythagorean Theorem. In our case,
AB^2 + AC^2 = BC^2
We know AC = 3sqrt(5) and BC = 4sqrt(5). Plug those numbers in to solve for AB like so:
AB^2 + [3sqrt(5)]^2 = [4sqrt(5)]^2
Now, solve (the “squared” must distribute to the 3 and the sqrt(5) on the left side, and same on the right side):
AB^2 + 9*5 = 16*5
AB^2 + 45 = 80
AB^2 = 35
AB = sqrt(35) Final answer.
2. Find the area of triangle ABC
Use AC as the base and AB as the height. Use the formula: Area = 1/2 * base * height
Area = 1/2 * AC * AB
Area = 1/2 * 3sqrt(5) * sqrt(35)
Area = 3/2 * sqrt(175) [you can multiply the 1/2 and the 3… And you can multiply the 5 by 35 inside of the square roots]
Now, you probably need to simplify the radical:
Area = 3/2 * sqrt(175) = 3/2 *sqrt(25*7) = 3/2 sqrt(25)*sqrt(7) = 3/2 * 5 * sqrt(7) = 15/2 * sqrt(7)
