Question

The length of a rectangle is three times its width. If we decrease the length by two meters and increase the width by 4 meters, the surface increases by 52m².Find the dimensions of the rectangle

Answer 1

Let the length of rectangle is l and width of the rectangle is w.

The area of rectangle obtained is

$A=l\times w$

It is given that length of rectangle is three times the width.

$l=3w$

It is also given that the length decrease by 2 m and width increase by 4 m andsurface increases by 52 sq.m.

$l\times w^{}+52=(l-2)(w+4)$

Now susbtitute the length equals to 3w in the equation.

$3w^2+52=lw+4l-2w-8$$3w^2+52=3w^2+12w-2w-8$$52=10w-8$$10w=60$$w=6m$

Therefore , the length of the rectangle is

$l=3\times6=18m$

Hence the length of rectangle is 18 m and width is 6m.