Question

The sum of ink in two squares is 468 sq m. The difference in their range is 24 metres, the arm of the square fort is removed.​

Answer 1

Answer:

Step-by-step explanation:

HEYA !

Let the side of two squares be 'a' and 'A'

Now

According to the question ,

Sum of Area of two square = 468 m²

a² + A² = 468 m² ----------(1)

[ ∵ Area of square = (side)² ]

Also,

Difference of their perimeter = 24 m

4A – 4a = 24 m

[ ∵ Perimeter of square = 4 × side ]

→ 4 ( A – a ) = 24

→ A – a = 6

→ A = 6 + a ---------(2)

Putting Value of A from (2) in (1) , We get

a² + (6 + a)² = 468

→ a² + 36 + a² + 12a = 468

→ 2a² + 12a + 36 – 468 = 0

→ 2a² + 12a – 432 = 0

→ a² + 6a – 216 = 0

→ a² + 18a – 12a – 216 = 0

→ a ( a + 18 ) – 12 ( a + 18 ) = 0

→ ( a – 12 ) ( a + 18 ) = 0

→ a – 12 = 0 ...or... a + 18 = 0

→ a = 12 ...or... a = – 18

Since , a = – 18 is not possible as side cannot be negative

Therefore ,

→ a = 12

Putting a = 12 in (2) , We get

A = 6 + 12 = 18

→ A = 18

Hence,