The length of a rectangle is 7 cm more than its width. If the diagonal of the rectangle is 35 cm, find the dimensions of the rectangle.
What is the width an length ?

Length = 12, width = 5

Step-by-step explanation:

The diagonal is the hypotenuse of a rectangular triangle.

Equation: d^2 = l^2 + w^2

35^2 = (x + 7)^2 + x^2

169 = (x + 7)(x + 7) + x^2

169 = x^2 + 7x + 7x + 49 + x^2

169 = 2x^2 + 14x + 49

subtract 169 from both sides

0 = 2x^2 + 14x - 120

divide by 2

0 = x^2 + 7x - 60

factor, to find the numbers just think of what number multiplied by what number would equal -60 and have the same numbers added together equals 7. 12 times 5 is 60 but it has to be -60, and 12 - 5 equals 7 so the numbers would be 12 and -5

0 = (x + 12)(x -5)

x = -12, and x = 5, but u can only use positive solutions so length equals 12 and width is 5

d

step-by-step explanation: