Question

the length of the rectangle is greater than the breadth by 18cm . if both length and breadth are increased by 6cm then area increase by 168cm square. find the length and breadth of the rectangle.

Answer 1

Let the length and breadth be L and B. L = B+18
Area = LB = A or
A = B(B+18) = B^2+18B …(1)
(B+6)(B+24) = A+168 …(2)
(B+6)(B+24) = B^2+18B+168, or
B^2+30B+144 = B^2+18B+168, or
12B = 24, or
B = 2 and L = 20
Check: LB= 2*20 = 40.
(L+6)(B+6) = 26*8=208 which is 208–40 = 168 more than the original area. Correct.
L = 20 cm and B = 2 cm.

Answer 2

$\huge\sf{\underline{\underline{Solution}}}$

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 :

If both length and breadth are increased by 6cm, then area increases by 168 cm^2

⇒ 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 2cm.