Question

The length of a rectangle exceeds it's width by 3m. If the width is increased by 4m and the length is decreased by 6m, the area is decreased by 22sq.m. Find the dimension of the rectangle

Answer 1

Area of the rectangle = Length * Width

Let x= Width of the rectangle

$x+3 =$ length of the rectangle

Area of the rectangle $= x(x+3) =x^2+3x$

Given that" the width is increased by 4m and the length is decreased by 6m"

Width is increased by 4 m $= x+4$

Length is decreased by 6 m $= x+3-6 =x-3$

Thus $(x+4)(x-3)=x^2+3x-22\\ x^2+4x-3x-12=x^2+3x-22$

Subtracting $x^2$ on both sides,

$x-12=3x-22$

Subtracting x on both sides,

$-12=2x-22$

Adding 22 on both sides, we get

$10=2x\\ 5=x$

Thus the width of the rectangle $= 5 m$

Length of the rectangle $= x+3= 5+3= 8 m$

Answer 2

Area of the rectangle = Length * Width

Let x= Width of the rectangle

length of the rectangle

Area of the rectangle  

Given that" the width is increased by 4m and the length is decreased by 6m"

Width is increased by 4 m  

Length is decreased by 6 m  

Thus  

Subtracting  on both sides,

Subtracting x on both sides,

Adding 22 on both sides, we get

Thus the width of the rectangle  

Length of the rectangle