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The length of a rectangle is 12 meters longer than half the width. The area of the rectangle is 90 square meters. Find the dimensions of the rectangle.
Step 1. Let w be the width.
Step 2. Let
be the length.
Step 3. Area
Step 4. Solving A in Step 3 yields the following steps.
Multiply 2 to both sides to get rid of denominator
Subtract 180 from both sides to get a quadratic equation
Step 5. To solve equation in Step 5, use the quadratic formula given below
where a=1, b=24, and c=-180
|Solved by pluggable solver: SOLVE quadratic equation with variable|
|Quadratic equation (in our case ) has the following solutons:|
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
Discriminant d=1296 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 6, -30.
Here's your graph:
. Area A=6*15=90 which is a true statement.
Step 6. ANSWER: The dimensions of a rectangle are 6 meters and 15 meters.
I hope the above steps were helpful.
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