CPM Homework Help : PC Problem 8-112

The circle below has a radius of 5 cm. The figure inscribed in the circle is a rectangle with width 2x. Express each of the following in terms of x. Homework Help ✎
1. The perimeter of the rectangle.
2. The area of the rectangle.

Step 1(a):

Draw a diagonal. If the radius is 5, how long is the diagonal?

Step 2(a):

Use the Pythagorean Theorem to find the length L.

$(2x)^2+L^2=10^2$

$L^2=100-4x^2$

$L=\sqrt{100-4x^2}$

$L=\sqrt{4(25-x^2)}$

$L=2\sqrt{25-x^2}$

Step 3(a):

Perimeter = 2(width) + 2(length)

Answer:

$\text{Perimeter}=2(2x)+2(2\sqrt{25-x^2})$

$\text{Perimeter}=4x+4\sqrt{25-x^2}$

Hint (b):

Area = (Length)(Width)

$\text{Area}=(2x)(2\sqrt{25-x^2})$

$\text{Area}=4x\sqrt{25-x^2}$

Answer (b):