Write the word or phrase that best completes each statement or answers the question.
-The area of a garden is 960 square feet, and the length of its diagonal is 52 feet. Find the dimensions of thegarden.
A)20 ft by 48 ft
B)5 ft by 192 ft
C)80 ft by 12 ft
D)60 ft by 16 ft

Question

Quizplus · Accepted Answer

The area of the garden is given by the formula for the area of a rectangle, which is length times width. The diagonal divides the rectangle into two right triangles, allowing us to use the Pythagorean theorem (a^2 + b^2 = c^2, where c is the length of the diagonal). We need to find two numbers (length and width) that when multiplied give 960 (the area) and also fit the Pythagorean theorem with 52 as the hypotenuse. Only the dimensions 20 ft by 48 ft satisfy both conditions: 20*48 = 960 and 20^2 + 48^2 = 400 + 2304 = 2704, which is the square of 52.

Write the Word or Phrase That Best Completes Each Statement