Question

A right triangular lawn, ABC, is surrounded on three sides by square shaped reading halls of a library X, Y, and Z, as shown below.
If the area of hall X is 25 square meters and the area of hall Z is 144 square meters, what is the area of hall Y?

Answer 1

A ) 169 square meters
B ) 289 square meters
C ) 119 square meters
D ) 150 square meters

Answer 2

Well if we know the areas of those squares, can you find the length of the sides?

Answer 3

if someone would show me how then probably

Answer 4

If we have a square and we know the side length, then the area is just the side-length squared. (A = s^2)

If we work backwards with the area, then the side-length is going to be the positive square root of the area, which just undoes the exponent. (sqrt(A) = sqrt(s^2) = s)

Answer 5

so it will be C?

Answer 6

Well, how did you get C? Here's what we're trying to do with that information:


Once we have the side-lengths, we can use Pythagorean theorem to find c^2, which interestingly is also the area of the square with side-length c