Answer:
Part A: D
Explanation:
Ok Let's assume you are right and the diagonal is 8x. If that is true, one of the answers will work.
Part A
It's the wrong answer. The answer is yes. Use a^2 + b^2 = c^It's the wrong answer. The answer is yes. Use a^2 + b^2 = c^It's the wrong answer. The answer is yes. Use a^2 + b^2 = c^2
givens
diagonal = 8x
one of the legs = 2x.
other leg = ?
Formula
a^2 + b^2 = c^2
(2x)^2 + b^2 = (8x^2) Expand the brackets
4x^2 + b^2 = 64x^2 Subtract 4x^2 from both sides.
b^2 = 64x^2 - 4x^2
b^2 = 60x^2
The prime factors of 60 are 2 * 2 * 3 * 5
You can't do much with the 3 and 5 so leave them under the root sign.
x^2 = x * x
What you get is
b^2 = √3 * 5 * 2* 2 * x * x
The factors come in pairs. One of the pairs goes outs the root. The other one is thrown away.
b = 2*x * √15
So the answer to part A is D
Part B
x = 3
The missing side = 2 * 3 * √15
The missing side = 6√15
The missing side = 23.2
Root 15 = 3.87