The area of a garden is 30 square feet. The perimeter is 26 feet. What are the measurements of each side?

Please help this question is fustrating

3 feet by 10 feet rectangle

Explanation:

Assuming this garden is a rectangle, it has dimensions L and W which are the length and width respectively.

perimeter of rectangle = 2*(length+width)

P = 2*(L+W)

26 = 2(L+W) ... plug in given perimeter

26/2 = L+W divide both sides by 2

13 = L+W

13-W = L   isolate L by subtracting W from both sides

L = 13-W

Area of rectangle = Length*Width

A = L*W

A = (13-W)W replace L with 13-W

A = W(13-W)

A = 13W - W^2 distribution

30 = 13W - W^2 plug in given area A = 30

W^2 - 13W + 30 = 0 ... get everything to one side

(W - 10)(W - 3) = 0 factor

W-10 = 0 or W-3 = 0 zero product property

W = 10 or W = 3

If the width is W = 10, then

L = 13-W

L = 13-10

L = 3 is the length

Or if the width is W = 3, then

L = 13-W

L = 13-3

L = 10 is the length

Either way, this is a 3 ft by 10 ft rectangle

Check:

Area = length*width = 10*3 = 30 square feet

perimeter = 2(length+width) = 2*(10+3) = 2*13 = 26 feet

or you could say

perimeter = L+W+L+W = 10+3+10+3 = 13+13 = 26 feet

we get the correct area and perimeter, so this confirms our answer.

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step-by-step explanation:

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