Question

A 20 x 32 rectangle is embedded inside a 98 x 108 rectangle. They share a vertex and their sides partially over lap as shown. Find the distance between the centers of the two rectangles.

Answer 1

The distance is 55 units.

Explanation:

Think of the bottom left corner of the rectangles, the shared vertex, as the origin of a coordinate plane. The positive x-axis is the lower 108-unit long horizontal side, and the positive y-axis is the left vertical 98-unit long side. The bottom left vertex is (0, 0). The center of the small rectangle is at (10, 16). The center of the large rectangle is at (54, 49). Now use the distance formula to find the distance between those two points.

`d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

`d = √((54 - 10)^2 + (49 - 16)^2)`

`d = √(44^2 + 33^2)`

`d = √(1936 + 1089)`

`d = √(3025)`

`d = 55`