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Since the perimeter equals the two lengths added to the two widths you can write this equation since you know the actual perimeter.

78cm = 2l + 2w

Since the area is the length multiplied by the width you can write this equation since you know the actual area.

108= lw

You have two variables (length and width) that you do not know. Sinceyou have two equations you can solve for the variables. you can use substitution or addition ifyou would like. I will use substitution.

l=108/w

78=2(108/w) + 2w

78=216/w + 2w

78w = 216 + 2w2

0 = 2w2 -78w + 216

w = 3cm or 36cm

now put both into the equations to find the length (l)

78 = 2l + 2(3 or 36)

78 = 2l + 6 or 72

2l = 72 or 6

l = 3cm or 36cm

Your dimensions are 36cm X 3cm

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Q: What are the dimensions of a rectangle with perimeter of 78cm and an area of 108cm?
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