Question

A rectangle has a length 10 m less than twice its width. When 3 m are added to the width, the resulting figure is a square with an area of 256 m?. Find the dimensions of the original rectangle.

Answer 1

....dimensions rectangle original:

x= width

2x-10 = the length

add 3m to the width = x+3

we obtain a square with a surface area of 256m².

square area =square²

(x+3)²= 256

x²+6x+9=256

x is calculated: x²+6x+9-256=0

x²+6x-247=0

b²-4ac =6²-4(1*-247)=1024

Δ =1024

Δ is strictly positive, so the equation x²+6x-247=0 has two solutions.

(-b-√Δ)/2a =(-6-32)/2=-19

(-b+√Δ)/2a =(-6+32)/2=13

an elongation is never negative, x = 13

width of initial rectangle: 13m

length of initial rectangle: 13*2-10=16m