SOLUTION: an open topped box has a square base (bottom)and a height of 7cm. if the surface area of the five sides of the box is 165cm squared, find the dimensionsof the square base?

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: an open topped box has a square base (bottom)and a height of 7cm. if the surface area of the five sides of the box is 165cm squared, find the dimensionsof the square base?      Log On

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Question 35738: an open topped box has a square base (bottom)and a height of 7cm. if the surface area of the five sides of the box is 165cm squared, find the dimensionsof the square base?
Answer by rapaljer(3742) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = edge of the square base.
x%5E2 = surface area of base
7x = surface area of each side, of which there are 4.

Total surface area = x%5E2+%2B+4%287x%29+=+165+

This is a quadratic equation, so set it equal to zero.
x%5E2+%2B+28x+-+165+=+0

These types of problems USUALLY factor, so try to find two factors of 165 such that the difference of the numbers is 28. Try 5 times 33!!
+%28x+%2B+33%29%28x-5%29+=+0
x=+-33 or x+=+5

Reject the negative answer since a side of a box cannot be negative. This leaves x = 5 for the side of the base. The base is 5 cm. by 5 cm.

R^2 at SCC