Question

The area of a rectangle is x2 + 7x + 12. If its breadth is (x + 3), then find its length. 2
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Answer 1

area of a rectangle = x² + 7x + 12

breadth of rectangle = (x+3)

We know that :-

Area of rectangle = length× breadth

Let length of given rectangle be L.

Now, according to the question :-

$\tt \implies L \times (x + 3) = {x}^{2} + 7x + 12$Now , x² + 7x + 12 can be written as :-

$\tt \longrightarrow {x}^{2} + 7x + 12 = {x}^{2} +3x + 4x + 12$

$\tt \longrightarrow {x}^{2} +3x + 4x + 12 = x(x +3) + 4(x + 3)$

$\tt \longrightarrow (x +3)(x + 4)$

$\tt \implies L \times (x + 3) = (x + 3)(x + 4)$

$\tt \implies L = \dfrac{ (x + 3)(x + 4)}{(x + 3)}$

$\tt \implies L = (x + 4) \:$

Therefore , length of rectangle = (x+4) units

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Learn more :

Area of circle = π r²

Area of square = (side)²

Area of rectangle = length × breath

Circumference of circle = 2πr

Perimeter of square = 4 × side

Perimeter of rectangle = 2( length+breadth)

Perimeter of any figure = sum of all sides of that figure

Answer 2

refer the attachment.......