The area of a rectangle is 52 in². the length of the rectangle is 9 in. longer than the width. what is the width of the rectangle? 3 in. 4 in. 6 in. 8 in.

Givens

Let the width = x

Let the length = x + 9

Area = 52 in^2

Formula

Area = L * W

Solve

52 = (x + 9)(x )            Remove the brackets.

52 = x^2 + 9x             Subtract 52 from both sides

x^2 + 9x - 52 = 0        Factor

You need 2 numbers that add to 9 and multiply to 52. There aren't many

52 and 1

26 and 2

13 and 4

All three will multiply to 52. 52 = 52 + 1 or 52 - 1 (The larger number must be plus). 53 or 51 is not the sum. 52 and 1 is not the answer.

26 and 2 will add or subtract to 28 or 24. Neither 1 is 9.  So that can't be your answer.

13 and 4 will give 9 or 17. There's your answer.

(x + 13)(x - 4) = 0

x = - 13 is not the answer. You cannot have minus distances.

x - 4 = 0

x = 4

The width is 4 inches  <<<< answer.

in the attachment.   i didn't see your choices.   the word which means there is choices.

step-by-step explanation:

(x,y)

x tells you how much left or right you go from the origin

y tells you how much down or up you go from the origin

so for example (-3,2), you go left 3 and up twice. i denoted which of the ordered pairs is which in my graph.