# Area is 350 square meter and the perimeter is 90 meter. What is the length of a rectangular pathway?

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Area = length * width

while

Perimeter = 2 (length + width) or P = 2L + 2W

So in order to find the length, we must compute first the width.

I will use the Perimeter.

So it will be like this,

90 = 2l + 2w

Divide both sides to two

45 = L + W

move length to left and change sign like this,

45 - L = W

therefore width is equal to 45 - length

We now use it to the Area.

Area is equal to 350 m^2

350 = L * (45 - L)

350 = 45L - L^2

move 45L - L^2 to the left and change sign

L^2 - 45L + 350 = 0

then factor

(L - 10) (L - 35)

therefore

L = 10 or 35

Since we are talking about rectangular, I suppose that 35 could be the length here and 10 will be the width.

I hope it helps.