Question

The perimeter of the original rectangle on the left is 30 meters. The perimeter of the reduced rectangle on the right is 24 meters. Not drawn to scale. What is x, the width of the original rectangle on the left? Round to the nearest hundredth if necessary.

a) 5 meters
b) 8 meters
c) 10 meters
d) 12 meters

Answer 1

To find the width of the original rectangle, set up a proportion using the perimeters of the two rectangles and solve a quadratic equation.

Step-by-step explanation:

To find the width of the original rectangle, we can set up a proportion using the perimeters of the two rectangles.

Let's say the original width of the rectangle on the left is x meters. So, its length will be (30 - 2x) meters, since the perimeter is the sum of all sides.

Similarly, the width of the reduced rectangle on the right is (x/2) meters, and its length is (24 - x) meters.

We can set up the proportion: (30 - 2x) / x = (24 - x) / (x/2)

Cross multiplying, we get: (30 - 2x) * (2/x) = (24 - x)

Simplifying, we have: 60 - 4x = 24x - x^2

Rearranging and simplifying further, we get: x^2 - 28x + 60 = 0

Now, we can solve this quadratic equation using factoring or the quadratic formula to find the value of x.

After solving, we find that x is approximately 5 meters.