SOLUTION: An open-topped box is made from a piece of cardboard measuring 20cm by 25cm. The sides of the box are formed by removing a square from each corner. The base of the box has an area

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: An open-topped box is made from a piece of cardboard measuring 20cm by 25cm. The sides of the box are formed by removing a square from each corner. The base of the box has an area       Log On


   

Question 1072656: An open-topped box is made from a piece of cardboard measuring 20cm by 25cm. The sides of the box are formed by removing a square from each corner. The base of the box has an area of 300cm^2.
a) Write an equation to represent the situation.
b) Use the quadratic formula to determine what amount needs to be removed from each side.
c) What are the dimensions of the box?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, the side length of each square corner to remove.


Area of the two dimensions for the base
%2820-2x%29%2825-2x%29=300

500-50x-40x%2B4x%5E2-300=0

4x%5E2-90x%2B200=0

x=%2890%2B-+sqrt%284900%29%29%2F8

x=%2890%2B-+70%29%2F8

Assuming the MINUS-form works better,
x=20%2F8
x=5%2F2
highlight%28x=2%261%2F2%29


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(The PLUS-form, giving x=20, will not work in the description.)