Question

The length of a rectangle is 9 cm more than the width. the area is 36 cm^2. find the length and width

Answer 1

Let the breadth of the rectangle be = x cm

Now length of rectangle = (x+9) cm

Area of rectangle is given as = 36 cm ²

As we know area of rectangle is l*b

Here length is x and breadth is (x+9) So area will be their product which is equal to 36 cm ²

x*(x+9)= 36

x²+9x=36

x²+9x-36=0

Now factorisation of this will be as follows ÷

x²+12x-3x-36=0

x(x+12)-3(x+12)=0

(x-3)(x+12)=0

Now as we know the zero method if the result obtained so is zero then one number should be equal to zero then only the result can be zero

So, let (x-3)= 0 which means x=3

(x+12)=0 here x= -12 and as we know the measure of side can't be negative so x= 3cm is the breadth of rectangle so length of rectangle = (3+9) cm= 12 cm

Answer 2

Answer:

let the length of rectangle be x

so the width will be x+9

l*b =Area of rectangle

x(x+9) = 36

x² +9x = 36

x²+ 9x -36= 0

x² +(12x - 3x) -36=0

x² + 12x - 3x -36 =0

x(x-3) +12(x-3)=0

(x+12)(x-3)

1. x = -12

but hence length canr be negative , length is 12.

2. x = 3

width =3