Solve Problems Using Systems of Nonlinear Equations
-A right triangle has an area of 36 square inches. The square of the hypotenuse is 145 . Find the lengths of the legs of the triangle. Round your answer to the nearest inch.
A) 8 inches and 9 inches
B) 64 inches and 81 inches
C) 4 inches and 18 inches
D) 16 inches and $4.5$ inches

Question

Quizplus · Accepted Answer

The area of a right triangle is given by $ \frac{1}{2} \times \text{base} \times \text{height} = 36 $. The Pythagorean theorem states that $ \text{base}^2 + \text{height}^2 = \text{hypotenuse}^2 $, and we're given the hypotenuse squared is 145. Solving these equations together, we find the base and height that satisfy both conditions are 9 and 8 inches, respectively.

Solve Problems Using Systems of Nonlinear Equations -A Right Triangle 4.54.54.5

Solve Problems Using Systems of Nonlinear Equations
-A Right Triangle $4.5$