Question

A rectangular patio measures 20 ft by 30 ft. You want to double the patio area by adding the same distance x to the length and width. Write and solve an equation to find a value for x, then find the new dimensions for the patio.

Answer 1

area = side x side = 20 x 30 =600 ft

we want to double the area, this is 1200 ft, therefore:

`\begin{gathered} \mleft(x+20\mright)\mleft(x+30\mright)=1200 \\ x^2+50x+600=1200 \\ x^2+50x-600=0 \\ \mleft(x+60\mright)\mleft(x-10\mright)=0 \\ x+60=0 \\ x=-60 \end{gathered}`

but, We don't measure in negative numbers, so we disregard this answer. and the other

`\begin{gathered} x-10=0 \\ x=10 \end{gathered}`

therefore, the patio is now 30ft x 40ft