The diagonal of a rectangular storage room is 4 yards long. If its length is 2 times its width, find the dimensions of the room.
w^2 + (2w)^2 = 4^2
5 w^2 = 16 etc
The diagonal of a rectangular storage room is 4 yards long. If its length is 2 times its width, find the dimensions of the room.
To find the dimensions of the rectangular storage room, let's use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's denote the length of the room as L and the width as W. According to the problem, the diagonal of the room is 4 yards long. We can form a right triangle with the diagonal as the hypotenuse.
Using the Pythagorean theorem, we have:
L^2 + W^2 = diagonal^2
Substituting the values, we get:
L^2 + W^2 = 4^2
Simplifying further, we have:
L^2 + W^2 = 16
We know from the problem that the length, L, is 2 times the width, W. So we can write:
L = 2W
Substituting this into the equation above, we get:
(2W)^2 + W^2 = 16
Simplifying, we have:
4W^2 + W^2 = 16
Combining like terms:
5W^2 = 16
Dividing both sides by 5, we get:
W^2 = 16/5
Taking the square root of both sides, we get:
W = √(16/5)
Similarly, using the equation L = 2W, we can calculate the length:
L = 2 * √(16/5)
Finally, we can approximate the values of L and W:
L ≈ 3.58 yards (rounded to two decimal places)
W ≈ 1.79 yards (rounded to two decimal places)
Therefore, the approximate dimensions of the rectangular storage room are approximately 3.58 yards in length and 1.79 yards in width.