Question

If the ore of Rectangle is x² + 5x+6.
find its length and breadth ?​

Answer 1

Answer:

The answer is -

Length(l) = (x + 2)

And,

Breadth(b) = (x + 3)

Step-by-step explanation:

To find the length and breadth

The ore(Area) of the rectangle = $x^{2}$ + 5x + 6[Given]

Step 1 = To find the length and breadth of the rectangle given in the question we have to factorize the ore of the rectangle

We know that Area of a rectangle = length(l) X breadth(b)

So, now equate the formula with the area of the rectangle given

And factorize the area of the rectangle given

That is,

l X b(L.H.S) =  $x^{2}$ + 5x + 6(R.H.S)

Factorize the area(or ore) through using identity (x + a)(x + b) =  $x^{2}$ +(a + b)x + ab

Find the factors of last term(6) which add up to middle term's constant(5)

That is,

2 X 3 = 6

2(a) + 3(b) = 5

Continue

l X b = $x^{2}$ + (2 + 3)x + 2 X 3

        =  $x^{2}$ + 2x + 3x + 2 X 3

Take common

        = x(x + 2) + 3(x +2)

Again take common

l[Length] X b[Breadth] = (x + 2)(x + 3)