Question

A rectangle has an area of 256 cm 2 . it has a width that is 48 cm shorter than 4 times its length. what is the rectangle's length?

Answer 1

let
x--------> the rectangle's length
y-------> the rectangle's width

we now that
Area of rectangle=x*y
Area=256 cm²
256=x*y-------> equation 1

y=4x-48------> y=4x-48------> equation 2

substitute equation 2 in equation 1

256=x*[4x-48]-----> 256=4x²-48x
4x²-48x-256=0

using a graph tool----> to resolve the second order equation
see the attached figure
the solution is
x=16 cm
y=4x-48----> y=4*16-48-----> y=16 cm

is a square

the answer is
the rectangle's length is 16 cm