Quadratic Word Problem About The Width Of A Basketball Court

Question

I was solving this problem from my algebra textbook:

A basketball court measures $25m \times 15m$. The court is surrounded by a row of benches that is the same width on all sides. If the row of benches has total area of $325m$$^2$, find the dimensions of the space needed for the court and benches. (Round answers to one decimal place if necessary)

I tried to solve the problem as follows:

Since we know the length of the benches we can call the width as $x$. Therefore we get the expression: $2(15x) + 2(25x) = 325$ and then you simply solve for $x$.

However, my answer was incorrect. Can somebody please help me solve the problem?

Answer 1

JaireetChahal I must say how you tackled the problem is ingenuous. But the classrooms are another matter :-\ .

If above were the case, then the way you solved would have given the correct value of $x$. Sadly it is not. Though, given the wording of the question, it should be valid.

Let's look at how you are required to see the problem.

Now, you should be able to work out the value of $x$ yourself and your attempt would be highly appreciable.

If you are still unable to get correct value of $x$ then look below:

Let the width of benches be $x$ metres.

We are given area of the red region as $325m$$^2=$ $(\text {Area of big rectangle})-(\text{Area of smaller rectangle})$.

$\Rightarrow 325 = (15+2x)(25+2x)-(15)(25)$

$\Rightarrow 325 = 4x^2+80x$

$\Rightarrow x=-10+\frac {5\sqrt { 29}}2=3.5 \text { (Approx.)}$

So, your classroom expects you to report $x$ as $3.5m$ instead of $4.1m$ as you were getting.