Solve.
-Mario's front patio is in the shape of a trapezoid with a height of 50 feet. The longer base is 11 feet longer than the shorter base, and the area of the patio is 10,000 square feet. Find the length of each Base of the trapezoidal patio.
A) 194.5 ft; 205.5 ft
B) 194.5 ft; 194.5 ft
C) 389 ft; 411 ft
D) 94.5 ft; 105.5 ft

Question

Quizplus · Accepted Answer

The area of a trapezoid is given by the formula A = (1/2) * (b1 + b2) * h, where b1 and b2 are the lengths of the two bases and h is the height. We are given that the area of the patio is 10,000 square feet and the height is 50 feet. We are also given that the longer base is 11 feet longer than the shorter base. Let x be the length of the shorter base. Then the length of the longer base is x + 11. Substituting these values into the formula for the area of a trapezoid, we get:10,000 = (1/2) * (x + x + 11) * 5010,000 = (1/2) * (2x + 11) * 5010,000 = (2x + 11) * 2510,000 = 50x + 2759,725 = 50xx = 194.5Therefore, the length of the shorter base is 194.5 feet and the length of the longer base is 194.5 + 11 = 205.5 feet.

Solve. -Mario's Front Patio Is in the Shape of a Trapezoid