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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?

The width of Zorns patio is labeled in the diagram below If the perimeter of the patio is 30x 26 feet what is the length of the patio class=

Respuesta :

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
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)

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