Question

The breath of a rectangle is 3cm longer than its length if the area is 180 find the dimension of the rectangle

Answer 1

Given :

• Breadth of Rectangle is 3 cm longer than its Length .
• Area of Rectangle is 180 cm² .

To Find :

• Dimensions of Rectangle .

Solution :

$\longmapsto\tt{Let\:Length\:be=x}$

As Given that Breadth of Rectangle is 3 cm longer than its length . So ,

$\longmapsto\tt{Breadth=x+3}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Rectangle=length\times{breadth}}$

Putting Values :

$\longmapsto\tt{180=x\times{x+3}}$

$\longmapsto\tt{180={x}^{2}+3}$

Now ,

$\longmapsto\tt{{x}^{2}+3-180}$

By Splitting Middle Term :

$\longmapsto\tt{{x}^{2}+(15x-12x)-180}$

$\longmapsto\tt{{x}^{2}+15x-12x-180}$

$\longmapsto\tt{x(x+15)-12(x+15)}$

$\longmapsto\tt{(x-12)\:\:(x+15)}$

• x = 12
• x = -15

As Dimensions can not be negative .So , The Value of x is 12 ...

Therefore :

$\longmapsto\tt\bf{Length=12\:cm}$

$\longmapsto\tt{Breadth=12+3}$

$\longmapsto\tt\bf{15\:cm}$

Answer 2

Answer:

$\sf\bold\red{AnswEr}$

★ Given :

• Breadth of rectangle is 3cm longer than the length .
• Area of rectangle is 180m² .

★ To find :

• Dimensions of rectangle

★ Solution :

Let , length of rectangle be x .

As given ,that breadth is 3cm longer than its length . So ,

$\sf{ Breadth = x + 3}$

★ Using formula :

$\red{\boxed{\ Area \: of\: rectangle = Length × Breadth }}$

★ Putting values :

$\sf{➙ 180 = x × x + 3}$

$\sf{➙ 180 = x² + 3}$

★ Now :

$\sf{➙ x² + 3 - 189}$

★ By splitting middle term :

$\sf{➙ x² + ( 15x - 12x ) - 180}$

$\sf{ ➙ x² + 15x - 12x - 180}$

$\sf{➙ x ( x + 15 ) - 12 ( x + 15 )}$

$\sf{ ( x - 12 ) ( x + 15 ) }$

• x = 12
• x = -15

As dimensions can not be negative .So , the value of x is 12.

★ Therefore :

• Length = 12cm
• Breadth = 12 + 3

$\sf{➙ 15 }$

∴ Hence , Breadth of rectangle is 15 cm .