The length of a rectangle is four times its width . If the length is decreased by 12 m , and the width increased by 12 m the rectangle become a square. Find the lengths of the sides of the original rectangle.
Answers
Answer:
Hi
Step-by-step explanation:
width = x
length = 4x
Dimensions of resulting square
width = x + 12
length = 4x - 12
Note that a square has equal measure of sides. This means that the length and width of the resulting square are equal to each other. We can set up an equation that represents this.
x + 12 = 4x - 12
Subtract x on both sides of equation.
12 = 3x - 12
Add 12 on both sides of equation.
24 = 3x
8 = x
Substitute this value into the dimensions of the original rectangle.
width = 8
length = 32
Let's change these values by their indicated increments to see if the sides become equal.
width: 8 + 12 = 20
length: 32 - 12 = 20
After changing the length and width of the rectangle, the dimensions became equal to each other. They have become a square. Thus, this checks out.
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