Question 255278
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.<br>
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<br>
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:
{{{d^2 = 14^2 + 9^2}}}
Simplifying the right side we get:
{{{d^2 = 196 + 81}}}
{{{d^2 = 277}}}
Solving for d we get:
d = +-{{{sqrt(277)}}}
Since d is the length of the diagonal, we will discard the negative value. So the length of the diagonal is {{{sqrt(277)}}}.