# SOLUTION: 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.

Algebra ->  Algebra  -> Rectangles -> SOLUTION: 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.      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Geometry: Rectangles Solvers Lessons Answers archive Quiz In Depth

Question 221567: 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.
You can put this solution on YOUR website!
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:

With , then . 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.