The area of a rectangular plank is 4500 cm². The plank was broken into two pieces, one of which is a square and the other a rectangle. What are the dimensions of the square if the length of the broken off rectangle is 120 cm?

1 Answer
Serena D.
Mar 17, 2018

30 cm (length), 30 cm (width)

Explanation:

Set up an equation with #x# representing the square's length/width (the square's dimensions are the same).

#x*(x+120)=4500 rarr# The width of the rectangular plank has to be the same as the square since the square was broken off of it (the plank), and the sum of the lengths of the rectangle and the square must add up to the length of the plank (these two parts originally formed part of the plank).

#x^2+120x=4500#

#x^2+120x-4500=0#

#(x-30)(x+150)=0 rarr# Think: two numbers that multiply to equal 4500 and that add up to 120

#x=30, -150 rarr# Disregard the -150 because a side length cannot be negative

The square is 30 by 30

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