In the diagram above, each circle is in contact two other circles and at least one side of the rectangle. The radii are perpendicular to the sides of the rectangle as shown. Find the area of the rectangle

Guest Jul 2, 2020

#2**+1 **

Let A = center of the top-left circle.

Let B = center of the top-right circle.

Let C = center of the bottom circle.

Draw AB; label the point of tangency of the two circle X.

Draw AC; its length is 24 + 16 = 40.

AX = 24.

Use the Pythagorean Theorem to find XC: XC^{2} + XA^{2} = AB^{2} ---> XC^{2} + 24^{2} = 40^{2}

Solving: XC = 32.

The width of the rectangle is 24 + 24 + 24 + 24 = 96

The height of the rectangle is: 24 + 32 + 16 = 72

From these two dimensions, you can find the area.

geno3141 Jul 2, 2020