QuestionA poster's length is 5 inches more than half its width, and its area is 48 square inches. Find the length and width.
Studdy Solution
STEP 1
Assumptions1. The length () of the poster is5 more inches than half its width (W). This can be written as L = W/ +5. The area (A) of the poster is48 square inches. The formula for the area of a rectangle is A = L * W3. We need to solve for the dimensions ( and W) of the poster.
STEP 2
We can substitute the expression for L from our first assumption into the formula for the area of a rectangle.
STEP 3
Now, plug in the given value for the area to get an equation in terms of W.
STEP 4
We can simplify this equation by distributing the W on the right side of the equation.
STEP 5
Multiply every term by2 to get rid of the fraction.
STEP 6
Rearrange the equation to a standard quadratic form, ax^2 + bx + c =0.
STEP 7
Now, we can solve this quadratic equation for W. We can use the quadratic formula, which is W = [-b ± sqrt(b^2 -4ac)] / (2a)
STEP 8
Calculate the value under the square root.
STEP 9
implify the equation.
STEP 10
Calculate the square root.
STEP 11
Now we have two possible solutions for W. Let's calculate both.
STEP 12
Since the width of a poster cannot be negative, we discard W2 = -16. So, the width of the poster is6 inches.
STEP 13
Now, we can find the length of the poster by substituting W =6 into the equation from our first assumption.
So, the dimensions of the poster are8 inches by6 inches.
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