Question

The width of Zorn’s patio is labeled in the diagram below. If the perimeter of the patio is (30x + 26) feet, what is the length of the patio?

Answer 1

Width = 7x + 4
Perimeter = (30x + 26)

Perimeter = 2( Length + Width)
30x + 26 = 2(Length + 7x + 4)

[Divide by 2 through]
15x + 13 = Length + 7x + 4

[Minus 7x on both sides]
15x + 13 - 7x = Length + 7x + 4 - 7x
8x + 3 = Length + 4

[Minus 4 on both sides]
8x + 13 - 4 = Length + 4 - 4
8x - 1 = Length

Length = 8x + 9 (Answer D)

Answer 2

Correct Option:
4th option is the correct answer

Solution:

The shape of Zorn's Patio is rectangular, as shown in the given image/ The perimeter of rectangle is calculated as:

Perimeter = 2 (Length + Width)

Width is given to be = (7x+4) feet
Perimeter is given to be = (30x+26) feet

Using the formula of perimeter we can write:

30x+26 = 2(Length + 7x+4)

Taking out 2 common from left hand side, we get:

2(15x+13) = 2(Length + 7x + 4)

Cancelling the common 2 from both sides, we get:

15x + 13 = Length + 7x + 4
⇒
Length = 15x + 13 - 7x -4
Length = 8x + 9

Therefore, the length of Zorn's Patio is (8x+9) feet