SOLUTION: Solving Problems with Quadratic Equations 21. An open-topped box is to be made from a rectangular piece of tin measuring 50 cm by 40 cm by cutting squares of equal size from each

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Question 815725: Solving Problems with Quadratic Equations
21. An open-topped box is to be made from a rectangular piece of tin measuring 50 cm by 40 cm by cutting squares of equal size from each corner. The base area is to be 875 cm^2.
a) Draw a diagram representing the information.
b) What is the side length of the squares being removed?
c) What is the volume of the box?
Thanks1!!
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
the base dimensions are 50 by 40
squares of side x are cut at the corners
the length will be (50-2x)
width will be (40-2x)
The area = 875 cm^2
(50-2x)((40-2x)=875
2000-180x+4x^2=875
4x^2-180x+1125=0
Find the roots of the equation by quadratic formula

a= 4 , b= -180 , c= 1125

b^2-4ac= 32400 + -18000
b^2-4ac= 14400
%09sqrt%28%0914400%09%29=%09120%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 180 + 120 )/ 8
x1= 37.50
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 180 -120 ) / 8
x2= 7.50
the side of square cut = 7.50 cm
Volume of box =50*40*7.50
=1500 cm^2