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

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) (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

x1=( 180 + 120 )/ 8
x1= 37.50

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
RELATED QUESTIONS
Solving Problems with Quadratic Equations 21. An open-topped box is to be made from a... (answered by josmiceli)

An open-topped box is made from a piece of cardboard measuring 20cm by 25cm. The sides of (answered by josgarithmetic)

An open box is to be made from a rectangular piece of tin by cutting 2-inch squares out... (answered by josgarithmetic)

an open topped box is made from a rectangular piece of cardboard, with the dimensions 24... (answered by checkley77,ankor@dixie-net.com)

An open box is to be made from a rectangular piece of tin by cutting two inch squares out (answered by ankor@dixie-net.com)

An open box is to be made from a rectangular piece of tin by cutting two inch squares out (answered by 303795)

An open box is to be made from a rectangular piece of tin by cutting two inch squares out (answered by checkley77)

Please help! I have been struggling with this question all morning! An open topped... (answered by josgarithmetic)

An open tin box is constructed from a rectangular piece of tin measuring 64 cm by 36 cm.... (answered by josgarithmetic)