Solve the problem.
-The area of a garden is 2160 square feet, and the length of its diagonal is 78 feet. Find the dimensions of the garden.

Question

Quizplus · Accepted Answer

The garden can be thought of as a rectangle, and the diagonal splits it into two right triangles. Using the Pythagorean theorem, $a^2 + b^2 = c^2$, where $c$ is the diagonal (78 feet) and $a$ and $b$ are the sides of the rectangle. Since the area is $ab = 2160$ square feet, we need to find values of $a$ and $b$ that satisfy both the area and the Pythagorean theorem. Only option A, with dimensions 30 feet by 72 feet, satisfies both conditions ($30^2 + 72^2 = 78^2$ and $30 \times 72 = 2160$).

Solve the Problem. -The Area of a Garden Is 2160 Square Feet, and Square