Find the dimensions of the room.

Question

The diagonal of a rectangular room is 52 ft long. One wall measures 28 ft longer than the adjacent wall. Find the dimensions of the room.

Answer 1

x^2 + (x+28)^2 = 52^2 Pythagorean Theorem

x^2 + x^2 + 2(28)x + 28^2 = 52^2 Expand

2x^2 + 56x + 784 = 2704

2x^2 + 56x - 1920 = 0

x^2 +. 28x - 960 = 0

x = [ - 28 =/- sqrt ( 28^2 - 4(a)(-960) ) ] / 2

x = [ -28 =/- 68 ] / 2

x = 40/2 = 20 Use positive solution.

Length of sides:

x = 20

(x + 28) = 48

Answer 2

52² = w² + (w + 28)²

Can you solve for w and answer?