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Step-by-step explanation:
Answer:
The length of the four pieces of protective strip is 96 feet
Step-by-step explanation:
Let the w be the width of the rectangular house and L is length. Since L = w + 16, its perimeter P = 2(w + L)
= 2(w + w + 16)
= 2(2w + 16)
Since the perimeter of the house P = 136 feet,
136 = 2(2w + 16)
dividing through by 2, we have
136/2 = (2w + 16)
68 = (2w + 16)
collecting like terms, we have
68 - 16 = 2w
52 = 2w
dividing through by 2, we have
w = 52/2
w = 26 feet.
Now, since the side walk is 3 foot wide all around, the width of the house plus sidewalk = w + 3 and the length of the house plus sidewalk = L + 3 = w + 16 + 3 = w + 19.
So, the perimeter of the house plus sidewalk which is the perimeter of the four pieces of protective strip is P' = 2(w + 3 + w + 19)
= 2(w + 22)
= 2(26 + 22)
= 2(48)
= 96 feet
So, the length of the four pieces of protective strip is 96 feet.
By definition of supplementary angles,
∠ABD + ∠BDE = 180
5x + 17x - 18 = 180
22x = 198
x = 9
∠ABD = 5(9) = 45°
∠BDE = 180 - 45 = 135°
Here it is I hope this is what u needed
