Question

The length of the rectangle is 5cm less than thrice its width. Find the dimensions of the rectangle if its area is 112cm²?

Answer 1

Let the width be x cm

Now, length =3x-5 cm

Area= (x) *(3x-5)

112=(3x-5)x

By factorization, we get

x=7 cm

Width is 7 cm and length is 16 cm

Answer 2

let the width of the rectangle be 'x'cm.

Therefore,length of the rectangle becomes '3x-5'cm.

From the given condition,

x(3x-5)=112.....(since,area of the rectangle is length x width)

x(3x-5)=112

3x^2-5x=112

3x^2-5x-112=0

3x^2-21x+16x-112=0

3x(x-7)+16(x-7))=0

(3x+16)(x-7)=0

either (3x+16)=0 or (x-7)=0

therefore x=-16/3 or x=7

but x=-16/3 is not acceptable since length of a rectangle cannot be negative.

therefore,

widht of the rectangle is x

=7cm

length of the rectangle is (3x-5)

=3(7)-5

=16 cm