The width of a rectangle is 12 cm less than the length the perimeter is 156 cm. find the length and width

We can write this question as an equation to solve it. Using L for length and W for width we know that

L+L+W+W=perimeter
2L+2W=perimeter

We can put the value of the perimeter into this

2L+2W=156cm

Next, we have to make sure all the terms (letters) are the same so we can solve it. This means we have to rewrite either the length or width in terms of the other.

We know the width is 12cm less than the length, which is the same as saying L-12
Then we substitute this into the equation and solve L

2L+2(L-12)=156
2L+2L-24=156
4L-24=156
4L=180
L=45cm

Next we use this value to find W.
45-12=33
W=33cm

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