Question

The breadth of a rectangle is 8 cm less than its length. If the length is increased by 4 cm and the breadth is increased by 9 cm, the area of the rectangle increases by 147 sq. cm. Find the length and breadth of the rectangle.​

Answer 1

Given :

• The breadth of a rectangle is 8 cm less than its length .
• If the length is increased by 4 cm and the breadth is increased by 9 cm, the area of the rectangle increases by 147 sq. cm.

To Find :

• Length and Breadth of the Rectangle .

Solution :

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

As Given that the breadth of a rectangle is 8 cm less than its length . So ,

$\longmapsto\tt{Breadth=x-8}$

$\longmapsto\tt{Area\:of\:Rectangle=x(x-8)}$

$\longmapsto\tt{{x}^{2}-8x}$

Also ,

• If the length is increased by 4 cm and the breadth is increased by 9 cm, the area of the rectangle increases by 147 cm² .

$\longmapsto\tt{Length=x+4}$

$\longmapsto\tt{Breadth=x-8+9=x+1}$

$\longmapsto\tt\bf{Area={x}^{2}-8x+147}$

Now ,

$\longmapsto\tt{(x+4)\:\:(x+1)={x}^{2}-8x+147}$

$\longmapsto\tt{{x}^{2}+x+4x+4={x}^{2}-8x+147}$

$\longmapsto\tt{{x}^{2}+5x+4={x}^{2}-8x+147}$

$\longmapsto\tt{{x}^{2}-{x}^{2}+5x+8x+4-147=0}$

$\longmapsto\tt{13x-143=0}$

$\longmapsto\tt{13x=143}$

$\longmapsto\tt{x=\cancel\dfrac{143}{13}}$

$\longmapsto\tt\bf{x=11}$

Value of x is 11 .

Therefore :

$\longmapsto\tt{Length\:of\:Rectangle=x}$

$\longmapsto\tt\bf{11\:cm}$

$\longmapsto\tt{Breadth\:of\:Rectangle=11-8}$

$\longmapsto\tt\bf{3\:cm}$

Answer 2

Answer :

• Length of rectangle is 11 cm
• Breadth of rectangle is 3 cm

Step-by-step explanation :

Given :

• The breadth of a rectangle is 8 cm less than its length.
• If the length is increased by 4 cm and the breadth is increased by 9 cm, the area of the rectangle increases by 147 cm².

To Find :

• Length and breadth of rectangle?

Solution :

• Let length of rectangle be y cm
• As it is stated in question that breadth of a rectangle is 8 cm less than its length. So, breadth of rectangle will be (y - 8) cm

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Finding area of rectangle by using formula of area of rectangle. As we know that,

◐ Area of rectangle = Length × Breadth

Putting all values,

⇒ Area of rectangle = y × (y - 8)

⇒ Area of rectangle = y(y - 8)

⇒ Area of rectangle = y² - 8y

Hence, area of rectangle is (y² - 8y) cm².

Now according to the question,

• If the length is increased by 4 cm and the breadth is increased by 9 cm, the area of the rectangle increases by 147 cm².

So,

• New length = (y + 4) cm
• New breadth = (y - 8 + 9) = (y + 1) cm
• New area = (y² - 8y + 147) cm²

Again using formula of area of rectangle. By putting all values in formula we get,

⇒ (y + 4) × (y + 1) = y² - 8y + 147

⇒ y(y + 1) + 4(y + 1) = y² - 8y + 147

⇒ y² + y + 4y + 4 = y² - 8y + 147

⇒ y² + 5y + 4 = y² - 8y + 147

⇒ y² - y² + 5y + 8y = 147 - 4

⇒ 0 + 13y = 143

⇒ 13y = 143

⇒ y = 143/13

⇒ y = 11

Hence, length of rectangle is 11 cm.

Now,

⇒ Breadth of rectangle = y - 8

Putting value of y in above equation,

⇒ Breadth of rectangle = 11 - 8

⇒ Breadth of rectangle = 3

Hence, breadth of rectangle is 3 cm.

Learn More :

• Perimeter of square = 4 × side
• Area of square = (side)²
• Perimeter of equilateral ∆ = 3 × side
• Area of equilateral ∆ = √3/4 (side)²
• Perimeter of rhombus = 4 × side
• Area of rhombus = ½ × d₁ × d₂
• Perimeter of circle = 2πr
• Area of circle = πr²
• Perimeter of rectangle = 2(l + b)
• Area of rectangle = l × b

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