Question

1.) The base of a parallelogram measures 7 centimeters more than its altitude. If thearea of the parallelogram is 30 square centimeters, find the measure of its baseand the measure of its altitude.

Answer 1

The area of a parallelogram is the product of the base and the altitude. in this case

`a(7+a)=30`

then solve the equation

`\begin{gathered} a(7+a)=30 \\ 7a+a^2=30 \\ 7a+a^2-30=30-30 \\ a^2+7a-30=0 \end{gathered}`
`\begin{gathered} \mleft(a-3\mright)\mleft(a+10\mright)=0 \\ a-3=0\quad \mathrm{or}\quad \: a+10=0 \\ a=3,\: a=-10 \end{gathered}`

therefore:

altitude = 3

base = 3 + 7 = 10