# SOLUTION: area of a rectangle is 243 m2. The height is nine less than 4 times the base. What is the perimeter?

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Question 209727: area of a rectangle is 243 m2. The height is nine less than 4 times the base. What is the perimeter?
Found 2 solutions by drj, MathTherapy:
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Area of a rectangle is 243 m^2. The height is nine less than 4 times the base. What is the perimeter?

Step 1. Let x be the base and 4x-9 be the height

Step 2. Perimeter P means adding up the four sides of a rectangle.

Step 3. Then

Step 4. Area=x*(4x-9)=243 or 4x^2-9x-243=0 or a quadratic equation.

Step 5. We can use the quadratic formula given as

where a=4, b=-9 and c=-243

 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=3969 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 9, -6.75. Here's your graph:

Select the positive number x=9.

Step 6. Then

Step 7. ANSWER: The perimeter is 81.

I just found this problem on 18 Sep 09, but I hope the above steps were helpful for review. Sorry about the late response.

And good luck in your studies!

Respectfully,
Dr J

You can put this solution on YOUR website!
area of a rectangle is 243 m2. The height is nine less than 4 times the base. What is the perimeter?

Let base of rectangle be B

Since the height is nine less than 4 times the base, then the height is 4B - 9

Since its area = 243m^2, we will have: B(4B - 9) = 243

B(4B - 9) - 243 = 0

(4B + 27)(B - 9) = 0

Therefore, 4B = - 27, or, B = 9

We will ignore the negative value as measuremnets CANNOT be negative

This means that B, or base = 9 meters

Now, since base = 9 meters, then height = 4(9) - 9, or, 27

Since base = 9 meters, and height = 27 meters, then perimeter = 2B + 2H ------> 2(9) + 2(27) ------> 18 + 54 = ( meters.