Wayne is hanging a string of lights 45 feet long around the three sides of his patio, which is adjacent to his house. The length of his patio, the side along the house, is five feet longer than twice its width. Find the length and width of the patio.

The length and width of the patio are 18¹/₃ feet and 6²/₃ feet respectively.

Step-by-step explanation:

Let L and W be the length and width of the patio respectively. Since the patio is a rectangle, its perimeter, P = 2(L + W). This perimeter equals the length of string of lights which is 45 ft.

Now, the length of his patio, the side along the house, is five feet longer than twice its width implies that L = 2W + 5.

Substituting L into P, we have

P = 2(L + W)

= 2(2W + 5 + W)

= 2(3W + 5)

= 6W + 5

Since P = 45 feet,

6W + 5 = 45

6W = 45 - 5

6W = 40

W = 40/6

W = 20/3 feet

W = 6²/₃ feet

Since L = 2W + 5, substituting W = 20/3 into L, we have

L = 2W + 5

= 2(20/3) + 5

= 40/3 + 5

taking the L.C.M, we have

= (40 + 15)/3

= 55/3 feet

= 18¹/₃ feet

So, the length and width of the patio are 18¹/₃ feet and 6²/₃ feet respectively.

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation:

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: