Question

Pick ONE of the two problems below to solve. The longest side of a trapezoid is 7 cm longer than the shortest side. The remaining two sides are both three times as long as the shortest side. If the perimeter of the trapezoid is 32 cm, write and solve an equation to find the lengths of all four sides of the trapezoid. Let s represent the length of the shortest side

Answer 1

Answer:

Let s be the length of the shortest side, then the length of the longest side is s+7cm, and the lengths of the remaining sides are both equal to 3s.

Now, recall that the perimeter of a trapezoid is the sum of the lengths of its sides, therefore we can set the following equation:

$s+7cm+s+3s+3s=32cm\text{.}$

Adding like terms in the above equation we get:

$8s+7cm=32cm\text{.}$

Subtracting 7cm from the above equation we get:

$\begin{gathered} 8s+7cm-7cm=32cm-7cm, \\ 8s=25cm. \end{gathered}$

Dividing the above equation by 8 we get:

$\begin{gathered} \frac{8s}{8}=\frac{25cm}{8}, \\ s=3.125cm\text{.} \end{gathered}$

Therefore the length of the shortest side is 3.125cm.

The length of the longest side is

$3.125\operatorname{cm}+7\operatorname{cm}=10.125\operatorname{cm}\text{.}$

The lengths of the remaining two sides are:

$3\times3.125\operatorname{cm}=9.375\operatorname{cm}\text{.}$