Question

suppose you have a rectangle where the length is greater than the width by 5 meters. the area of the rectangle is 300m2. what is the perimeter? (1 point)

Explanation:

Step1: Define variables

Let the width of the rectangle be $x$ meters. Then the length is $x + 5$ meters.

Step2: Set up area - equation

The area formula of a rectangle is $A=\text{length}\times\text{width}$. So we have $x(x + 5)=300$.
Expanding gives $x^{2}+5x-300 = 0$.

Step3: Solve the quadratic equation

For the quadratic equation $ax^{2}+bx + c=0$ ($a = 1$, $b = 5$, $c=-300$), we use the quadratic formula $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.
First, calculate the discriminant $\Delta=b^{2}-4ac=(5)^{2}-4\times1\times(-300)=25 + 1200 = 1225$.
Then $x=\frac{-5\pm\sqrt{1225}}{2}=\frac{-5\pm35}{2}$.
We get two solutions: $x_1=\frac{-5 + 35}{2}=15$ and $x_2=\frac{-5-35}{2}=-20$. Since the width cannot be negative, we take $x = 15$ meters.

Step4: Find the length

The length is $x + 5=15 + 5=20$ meters.

Step5: Calculate the perimeter

The perimeter formula of a rectangle is $P = 2(\text{length}+\text{width})$.
So $P=2(20 + 15)=2\times35 = 70$ meters.

Answer:

70 meters