Question

A rectangle is 8 cm longer than its width A square of side x cm has been cut our of it If x cm is half the width of the rectangle then the remaining area is

• A. $(2x^2+8x)c{m}^2$
• B. $(2x^2+16x)c{m}^2$
• C. $(3x^2+8x)c{m}^2$
• D. $(3x^2+16x)c{m}^2$

Answer 1

The correct option is D $(3x^2+16x)c{m}^2$

Let the width of rectangle is y cm then length of rectangle is y+8 cm

Then area of total rectangle =$y(y+8)=y^2+8yc{m}^2$

If a square side x cm cut in this rectangle whose side is half of width of rectangle

So x=\frac{1}{2}y \Rightarrow y=2x$

Then area of total rectangle =$y(y+8)=y^2+8yc{m}^2$ put the value y=2x

Then area of rectangle=$2x(2x+8)=4x^2+16xc{m}^2$

Then renaming area =$4x^2+16x-x^2=(3x^2+16x)c{m}^2$