Solve Problems Using Systems of Nonlinear Equations
-The area of a garden is 432 square feet, and the length of its diagonal is 30 feet. Find the dimensions of the garden.
A) 18 feet by 24 feet
B) 3 feet by 144 feet
C) 108 feet by 4 feet
D) 12 feet by 36 feet

Question

Quizplus · Accepted Answer

The garden can be represented as a rectangle with area $A = lw = 432$ square feet, where $l$ and $w$ are the length and width, respectively. The diagonal $d = 30$ feet forms a right triangle with the length and width, so by the Pythagorean theorem, $l^2 + w^2 = d^2 = 900$. Solving the system of equations $lw = 432$ and $l^2 + w^2 = 900$ leads to the dimensions $l = 24$ and $w = 18$, making the correct answer 18 feet by 24 feet.