The lenght of one base of a trapezoid is 19 less than five times the length of the other base. If the trapezoid has a height of 18 feet and an area of 477 ft2, find the length of the longer base

(12+5×12−19)÷2×18=477

12

Chrisambriz57

To find the length of the longer base of the trapezoid, we can use the formula for the area of a trapezoid:

Area = (1/2) * (b1 + b2) * h

Where:
b1 = length of the shorter base
b2 = length of the longer base
h = height of the trapezoid

We are given that the height (h) is 18 feet and the area is 477 ft². We need to solve for b2.

Substituting the known values into the formula, we get:

477 = (1/2) * (b1 + b2) * 18

Now, let's find the expression for b1 in terms of b2. We are given that the length of one base (b1) is 19 less than five times the length of the other base (b2), so we can write:

b1 = 5b2 - 19

Substituting this expression for b1 into the area formula, we have:

477 = (1/2) * (5b2 - 19 + b2) * 18

To simplify, let's first combine like terms inside the parentheses:

477 = (1/2) * (6b2 - 19) * 18

Next, distribute the factor of 18 to the terms inside the parentheses:

477 = (1/2) * 108b2 - (1/2) * 342

Now, simplify further:

477 = 54b2 - 171

To isolate the variable, let's add 171 to both sides:

477 + 171 = 54b2

648 = 54b2

Now, divide both sides by 54 to solve for b2:

648 / 54 = b2
12 = b2

Therefore, the length of the longer base (b2) is 12 feet.

(x + 5x-19)/2 * 18 = 477

find x, the shorter base, then 5x-19, the longer base