a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?

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a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?

We know the rectangle has the following formulas:
Area = lw
Perimeter = 2l + 2w

Given an area of 238 and a perimeter of 62, we have:

1. lw = 238
2. 2(l + w) = 62

Divide each side of (1) by w:
l = 238/w

Substitute this into (2):
2(238/w + w) = 62

Divide each side by 2:
238/w + w = 31

Multiply each side by w:
238w/w + w^2 = 31w

Simplify:
238 + w^2 = 31w

Subtract 31w from each side:
w^2 - 31w + 238 = 0

We have a quadratic. So we run this through our quadratic equation calculator and we get:
w = (14, 17)

We take the lower amount as our width and the higher amount as our length:
w = 14
l = 17

Check our work for Area:
14(17) = 238 <-- Check

Check our work for Perimeter:
2(17 + 14) ? 62
2(31) ? 62
62 = 62 <-- Check