SOLUTION: It took 72 square feet of Tyvek house wrap to cover a trapezoid-shaped part of a house. Find the height of the trapezoid if the length of its shorter base is the same as its height

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Question 1153532: It took 72 square feet of Tyvek house wrap to cover a trapezoid-shaped part of a house. Find the height of the trapezoid if the length of its shorter base is the same as its height. (The formula for the area of a trapezoid is
A = 1/2 h (b (sub) 1 + b (sub) 2)
, where h is its height, and b1 and b2 are the lengths of the two bases.)
FInd the height!
There is a little illustration of a trapezoid that says the longest base is 18 ft. If you want to see the illustration, reply to me wiht your email and ill send it your way. Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

The answer is 6 feet

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How to get this answer:

h = height
b1 = longer base = 18 ft
b2 = shorter base = h
A = area of trapezoid = 72 square ft

A+=+%28h%2A%28b1%2Bb2%29%29%2F2 area of trapezoid formula

72+=+%28h%2A%2818%2Bh%29%29%2F2 plug in given values

72%2A2+=+h%2A%2818%2Bh%29 Multiply both sides by 2

144+=+18h%2Bh%5E2 Distribute

0+=+18h%2Bh%5E2-144 Subtract 144 from both sides

0+=+h%5E2%2B18h-144

h%5E2%2B18h-144+=+0 Get equation into standard form

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Use the quadratic formula to solve for h
We will plug in: a = 1, b = 18, c = -144

h+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 or h+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29

h+=+%28-18%2Bsqrt%28%2818%29%5E2-4%281%29%28-144%29%29%29%2F%282%281%29%29 or h+=+%28-18-sqrt%28%2818%29%5E2-4%281%29%28-144%29%29%29%2F%282%281%29%29

h+=+%28-18%2Bsqrt%28900%29%29%2F%282%29 or h+=+%28-18-sqrt%28900%29%29%2F%282%29

h+=+%28-18%2B30%29%2F%282%29 or h+=+%28-18-30%29%2F%282%29

h+=+%2812%29%2F%282%29 or h+=+%28-48%29%2F%282%29

h+=+6 or h+=+-24

Ignore the negative solution for h. A negative height does not make sense.

The only possible height value is h = 6.
Therefore, the shorter base is also 6 ft long.

Let's check to see if b1 = 18, b2 = 6, and h = 6 all lead to an area of 72
A+=+%28h%2A%28b1%2Bb2%29%29%2F2

A+=+%286%2A%2818%2B6%29%29%2F2

A+=+%286%2A24%29%2F2

A+=+144%2F2

A+=+72

The answer is confirmed.