SOLUTION: the trapezoid has an area of 48cm squared. find the value of x the height is x+1 base is x+6 and base is x

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Question 35675: the trapezoid has an area of 48cm squared. find the value of x the height is x+1 base is x+6 and base is x
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the area of a trapezoid:
A+=+%28%28b1+%2B+b2%29%2F2%29h
In your problem:
A = 48 sq.cm.
b1 = x+6
b2 = x
h = x+1
48+=+%28%28%28x%2B6%29%2B%28x%29%29%2F2%29%28x%2B1%29 Simplify.
48+=+%28%282x%2B6%29%2F2%29%28x%2B1%29 Factor a 2 in the top.
48+=+%282%28x%2B3%29%2F2%29%28x%2B1%29 Cancel the 2s.
48+=+%28x%2B3%29%28x%2B1%29 Perform the indicated multiplication.
48+=+x%5E2%2B4x%2B3 Subtract 48 from both sides of the equation.
x%5E2%2B4x-45+=+0 Solve for x by factoring.
%28x-5%29%28x%2B9%29+=+0 Apply the zero products principle.
x-5+=+0 and/or x%2B9+=+0
If x-5+=+0 then x+=+5 This is an acceptable solution as it is positive.
If x%2B9+=+0 then x+=+-9 This is not meaningful as the length of the base has to be a positive value.
Answer:
x = 5 cm.