Question

The length of one base of a trapezoid is 7mm less than twice the length of the other base. The height of the trapezoid is 12mm. The area of the trapezoid is 48 square mm. Find the length in millimeters of the longer base. (Please show step by step)

Answer 1

Answer:

The length of the longer base is 5mm.

Step-by-step explanation:

The area of a trapezoid:

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

With the given information, we can write some equations to represent the problem:

$b_1=2b_2-7\\48=\frac{1}{2}(12)(b_1+b_2)$

There's only 2 equations and 2 variables, so it's a relatively simple system of equations to solve. Ill solve by substitution:

$b_1=2b_2-7\\48=\frac{1}{2}(12)(b_1+b_2)\\\\48=\frac{1}{2}(12)((2b_2-7)+b_2)\\48=(6)(3b_2-7)\\48=18b_2-42\\18b_2=90\\b_2=5$

Now, plug that back into the first equation to solve for the other variable:

$b_2=5\\b_1=2b_2-7\\\\b_1=2(5)-7\\b_1=10-7\\b_1=3$

Now we have the measures of both of the bases.

• the longer base = 5mm
• the shorter base = 3mm

To check that, calculate the area using these bases:

$A=\frac{1}{2}(12)(3+5)\\A=6(8)\\A=48$

It works fine.