Question

A rectangular room has an area of 315 square feet. the length is 6 feet more than the width. find the dimensions of the room.

Answer 1

Width - x ft.
Length - (x+6)ft.

x(x+6)=315
x²+6x-315=0
a=1, b=6, c=-315

D=b²-4ac=36+4*1*315=1296, √D=√1296=36


`x = (-b+/- √(D) )/(2a) \\ \\ x= (-6+/-36)/(2) \\ \\ x=15, x=-21`

For the width we can use only positive number.
The width =15 ft.
The length =15+6=21 ft.

Check :
Area =15*21=315 ft²