SOLUTION: The length of a rectangle is x + 4 The width of a rectangle is x - 1 The perimeter is 46 cm Calculate the length of the diagonal of the rectangle Please help?!

Question 255278: The length of a rectangle is x + 4
The width of a rectangle is x - 1
The perimeter is 46 cm
Calculate the length of the diagonal of the rectangle

Please help?!
Found 2 solutions by drk, jsmallt9:
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
The length of a rectangle is x + 4
The width of a rectangle is x - 1
The perimeter is 46 cm
--
We can use th perimter formula as:
(i)
replacing x + 4 for L, x - 1 for W, and 46 for P, we get
(ii)
we solve for x as
(iii)
(iv)
(v)
(vi)
Now, the length = 14, and the width is 9.
--
Using the Pythagorean theorem:

we get

the diagonal, c, ~ 16.64
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
If we know the length and width of a rectangle we can use the Pythagorean Theorem to find the diagonal. So we will start by finding the length and width.

We should know that the perimeter of a rectangle is the sum of the two lengths and the two widths. We are told that the perimeter is 46 and that the length is x+4 and the width is x-1. So:
46 = x+4 + x+4 + x-1 + x-1
We can solve this for x. Simplifying the right side we get:
46 = 4x + 6
Subtracting 6 from each side we get:
40 = 4x
Dividing both sides by 4 we get:
10 = x

So the length, x+4, is 14 and the width, x-1, is 9. The length and width of a rectangle and the diagonal of a rectangle form a right triangle with the diagonal as the hypotenuse. So we can use the Pythagorean Theorem to find the length of the diagonal. If d is the length of the diagonal then:

Simplifying the right side we get:

Solving for d we get:
d = +-
Since d is the length of the diagonal, we will discard the negative value. So the length of the diagonal is .

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