Question

A landscaper is designing a flower garden in the shape of a trapezoid. She wants the length of the shorter base to be 3 yards greater than the height, and the length of the longer base to be 5 yards greater than the height. For what height will the garden have an area of 375 square yards? Round to the nearest tenth of a yard.

a. 155.7 yards
c. 39.9 yards
b. 17.5 yards
d. 34.9 yards

Answer 1

To find the height of the trapezoid garden, you need to set up an equation using the area formula for a trapezoid, solve the quadratic equation, and round the height to the nearest tenth of a yard.

Step-by-step explanation:

To find the height of the trapezoid garden, we need to set up an equation using the area formula for a trapezoid: Area = (1/2) * height * (base1 + base2).

Given that the shorter base length is 3 yards greater than the height (let's call it x) and the longer base length is 5 yards greater than the height, we can substitute these expressions into the area formula as follows:

375 = (1/2) * x * (x + x + 5).

Simplifying the equation, we get:

750 = x^2 + 5x.

Now, let's solve this quadratic equation:

1. Rearrange the equation to get it in standard quadratic form: x^2 + 5x - 750 = 0.
2. Factor the quadratic equation if possible, otherwise use the quadratic formula.
3. Calculate the height (x) using the factored equation or the quadratic formula.
4. Round the height to the nearest tenth of a yard.

After solving, we find that the height of the garden is approximately 17.5 yards, so the correct answer is b. 17.5 yards.