The length of a rectangle is 5 more than the width. Find the length and width of a rectangle if the area of the rectangle is 36 inches.

width = 4 in

length = 9 in

Step-by-step explanation:

To solve this problem, write an expression for the length and use the area of a rectangle formula.

The formula for area of a triangle is A = lw

"A" is the area.

"l" is the length.

"w" is the width.

"The length of a rectangle is 5 more than the width". It is represented in an expression:

l = w + 5 The width plus 5 is the length.

We also know the area is 36 in². Using information we know, replace variables in the formula for area of a rectangle.

Substitute l = w + 5 and A = 36

A = lw

36 = (w + 5) w Expand by multiplying w by the terms in the brackets.

36 = w² + 5w Since the equation is quadratic, make it equate to 0.

36 - 36 = w² + 5w - 36 Subtract 36 from both sides

0 = w² + 5w - 36 Factor this. Use group factoring, which is when you replace the middle term (5w) with two terms that add to make 5w, and multiply to get the last term (-36).

0 = w² + 9w - 4w - 36 9w times - 4w is - 36. They also add to get 5w.

0 = (w² + 9w) + (-4w - 36) Group the factors

0 = w (w + 9) + - 4 (w + 9) Take out the common factor in each group.

0 = w (w + 9) + - 4 (w + 9) Take out the new common factor binomial w+9

0 = (w + 9) (w - 4) Fully factored equation.

w + 9 = 0 w - 4 = 0 Set each binomial to equal 0.

w = - 9 w = 4 Chose what makes sense to be the width.

The width cannot be a negative number, so the width is 4.

Since we know the width, we can find the length because the length is 5 more than the width.

l = w + 5

l = 4 + 5

l = 9 Length of the rectangle

Don't forget to include the units, inches.

Therefore the length is 9 inches and the width is 4 inches.