Question

A backyard is in the shape of a trapezoid with height of 55 feet. The shorter base is 12 feet shorter than the longer​ base, and the area of the backyard is 1650 square feet. Find the length of each base of the trapezoidal yard.

Answer 1

Answer : The length of each base of the trapezoidal yard are, 36 and 24 feet.

Explanation :

Let the longer base of trapezoid be, x

So, the shorter base of trapezoid is, (x-12)

As we are given that:

Area of trapezoid = 1650 square feet

Formula for the area of trapezoid is:

$A=\frac{1}{2}\times (b_1+b_2)\times h$

where,

A = area of trapezoid

$b_1$ = longer base length

$b_2$ = shorter base length

h = height

Now put all the given values in the above formula, we get:

$1650=\frac{1}{2}\times (x+(x-12))\times 55$

By the solving the terms, we get the value of 'x'.

x = 36

Thus, the value of x = 36 feet

The longer base of trapezoid = x = 36 feet

The shorter base of trapezoid = (x-12) = 36 - 12 = 24 feet

Thus, the length of each base of the trapezoidal yard are, 36 and 24 feet.

Answer 2

Answer:

The length of each base of the trapezoidal yard are, 36 and 24 feet.

Explanation :

Let the longer base of trapezoid be, x

So, the shorter base of trapezoid is, (x-12)

As we are given that:

Area of trapezoid = 1650 square feet

Formula for the area of trapezoid is:

where,

A = area of trapezoid

= longer base length

= shorter base length

h = height

Now put all the given values in the above formula, we get:

By the solving the terms, we get the value of 'x'.

x = 36

Thus, the value of x = 36 feet

The longer base of trapezoid = x = 36 feet

The shorter base of trapezoid = (x-12) = 36 - 12 = 24 feet

Thus, the length of each base of the trapezoidal yard are, 36 and 24 feet.

Explanation: