SOLUTION: An open box is made from a 30​-cm by 80​-cm piece of tin by cutting a square from each corner and folding up the edges. The area of the resulting base is 1776cm^2. What is th

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Question 1137244: An open box is made from a 30​-cm by 80​-cm piece of tin by cutting a square from each corner and folding up the edges. The area of the resulting base is
1776cm^2. What is the length of the sides of the​ squares in cm?
Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
.
Mathematical model is this equation


    (30-2x)*(80-2x) = 1776,


where x is the length of the square under the question.


Simplify and solve, step by step


    2400 - 160x - 60x + 4x^2 = 1776

    4x^2 - 220x + 2400 - 1776 = 0

    4x^2 - 220x + 624 = 0

    x^2 - 55x + 156 = 0

    x%5B1%2C2%5D = %2855+%2B-+sqrt%2855%5E2+-+4%2A156%29%29%2F2 = %2855+%2B-+49%29%2F2.


The two roots are  52  and  3.

Of them, only x= 3 is meaningful.


(The other root x= 52 makes the dimensions of the new base negative !).


ANSWER.  the side of the square is 3 cm.


CHECK.   (30-2*3)*(80-2*3) = 24*74 = 1776 square centimeters.   ! Correct !

Solved.