Solve this problem using the proper formula. A lot is in the shape of a trapezoid. The sum of the bases is 280 feet. If the area of the lot is 8,400 square feet, what is the distance across the lot, i. e., the altitude of the figure? The altitude of the trapezoid is feet.

9514 1404 393

  60 ft

Step-by-step explanation:

The formula for the area of a trapezoid is ...

  A = 1/2(b1 +b2)h

Fill in the given information and solve for h.

  8400 ft² = (1/2)(280 ft)h

  h = 8400 ft²/(140 ft) = 60 ft

The altitude of the trapezoid is 60 feet.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

d. you cannot tell because there are no values shown.