A poster length is three more than two times its width and the area of the poster is 152 square inches

Question

A poster length is three more than two times its width and the area of the poster is 152 square inches. Find the width and length of the poster.

Answer 1

Write equations to describe the situation:

L = 2W + 3

A = 152

Remember that the formula for area of a rectangle is:

A = 2L + 2W

Place your known values into the A = 2L + 2W equation.

---> 152 = 2(2W + 3) + 2W <---

See that we've replaced the A with 152 and replaced the L with (2W + 3).

Now you can solve the W because you only have one variable. Distribute the 2 that's outside parentheses, combine like terms, and solve using algebra (subtract on both sides, divide on both sides). Now that you've found the value of W, you can find L by doing 2W + 3 sine that is what they said the length was.

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Answer 2

L= 3 + 2W

A=LW = 152 = (3+2W)W = 3W + 2W^2

2W^2 + 3W -152 = 0

(2W+19)(W-8) = 0

W = 8 inches

L = 3+16 = 19 inches