A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. the total area of the flower garden is 150 square yards. what will the length of each base be
Answers
18 yards and 22 yards are the length of trapezoid.
What is Trapezoid?
Trapezoids are quadrilaterals that have two parallel sides and two non-parallel sides
Given,
shorter base to be 3 yards greater than the height
b₁=h+3
longer base to be 7 yards greater than the height.
b₂=h+7
Area of trapezoid=1/2(b₁+b₂)h
150=1/2(h+3+h+7)h
150=(2h+10)h/2
150=2h²+10h/2
150=2h²+5h
h²+5h-150=0
h²+15h-10h-150=0
h(h+15)-10(h+15)=0
(h-10)(h+15)=0
h=10 or h-15
h value should be positive.
So b₁=h+3=15+3=18
b₂=h+7=15+7=22
Hence the bases be 18 yards and 22 yards.
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Let shorter base = h +3 and longer base = h + 7 where h is the height.
Formula for area of a trapezoid is
Substituting into the formula we get the following equation.
This is a quadratic equation which I will solve by factoring.
so shorter base = 10 + 3 = 13 yards and longer base = 10 + 7 = 17 yards
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Answers
If the width is 5m longer than the length,
Then Perimeter = 2(l + 5) + 2l
= 4l + 10 {THE EQUATION}
Since Perimeter = 58 m
Then 4l + 10 = 58 m
⇒ l = 12 m
Thus the Length of the Pool = 12 m