Question

the length of a rectangle is graeter than the breadth by 18cm. if both length and breadth are increased by 6cm , then area increases by 168cm sq. find the length and breadth of the rectangle​

Answer 1

AnswEr :

Let the Breadth of Rectangle be a cm and Length be (a + 18) cm.

⇝ Area of Rectangle = Length × Breadth

⇝ Area of Rectangle = (a + 18) × a

⇝ Area of Rectangle = (a² + 18a) cm²

• According to the Question Now :

If both length and breadth are increased by 6cm, then area increases by 168 cm²

⇒ Area = Length × Breadth

⇒ (a² + 18a) + 168 = (a + 18 + 6) × (a + 6)

⇒ a² + 18a + 168 = (a + 24)(a + 6)

⇒ a² + 18a + 168 = a(a + 24) + 6(a + 24)

⇒ a² + 18a + 168 = a² + 24a + 6a + 144

⇒ a² + 18a + 168 = a² + 30a + 144

⇒ a² - a² + 168 - 144 = 30a - 18a

⇒ 24 = 12a

• Dividing Both term by 12

⇒ a = 2 cm

◗ Breadth = a = 2 cm

◗ Length = (a + 18) = (2 + 18) = 20 cm

∴ Length is 20 cm and Breadth is 2 cm.

Answer 2

Given :------

• Length is 18cm greater than breadth .
• if length and breadth increased by 6cm , area increased by = 168cm²

To Find :---

• Length and breadth of Rectangle ?

Formula used :----

• Area of Rectangle = length × breadth
• (a+b)² = (a² + 2ab+b²)

Solution :-------

Let Breadth of rectangle = x cm

than its length = (x+18)cm

Area of rectangle = l × b = x(x+18) cm²

Now, breadth and length is increased by = 6m

New breadth = (x+6)cm

New length = (x+18+6) = (x+24)cm²

New area = (x+6)(x+24)cm²

A/q,

it is given that, new area is increased by 168cm² ,,

so,

[(x+6)(x+24)] - [x(x+18)] = 168

➾ [ x²+24x+6x+144] - [x²+18x] = 168

➾ [x²+30x+144-x²-18x] = 168

➾ 12x = 168 - 144

➾ 12x = 24

➾ x = 2cm = Breadth of rectangle .

➾ x + 18 = 20cm = Length of rectangle .

⛬ length and breadth of rectangle are 20cm and 2cm .

(Hope it helps you)