Question

Please answer this question
Two square area sum is 468m^2.difference of their perimeter is 24m.Find the sides of both.​

Answer 1

Question :-

Two squares of area sum is 468m² difference of their perimeter is 24m.Find the sides of both.

Answer :-

Side of square (1) is 18 metre and side of square (2) is 12 metre.

To find :-

→ Side of square

Formula used :-

→ Perimeter of square = 4 × side

→ Area of square = (side)²

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Explanation :-

Given that ,

• Sum of area of two square is 468 m²

•difference of their perimeter is 24m

Let the side of square (1) be "a" metre

Perimeter of square (1) = 4a

According to the question,

→ difference of both perimeter = 24

→ perimeter of square[ (1) - (2)]= 24

→ 4a - perimeter of square (2) = 24

→ perimeter of square (2) = 4a -24

Let the side of square (2) is "b" metre

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We know that,

• perimeter of square (2) = 4a-24

→4{side of square (2) } = 4a -24

→ 4b = 4a - 24

→ b = a - 6 .....eq.(1)

now we have ,

[ side of square (1) is "a" and side of square (2) is " a - 6 ",

according to the condition,

• Sum of their areas = 468

→ (a)² + (a - 6)² = 468

→ a² +a² +36 - 12a = 468

→ 2a² - 12a -432 = 0

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solve this Quadratic equation,

→ 2[ a² - 6a -116] = 0

→a² - 6a -116 = 0

→ a² - 18a + 12a -116 = 0

→a (a -18 ) +12 (a - 18) = 0

→(a -18)(a+12) = 0

• Case 1

when,

→ a - 18 = 0

→ a = 18

• Case 2

when,

→a +12 = 0

→ a = -12

We know that side of any square can't be negative therefore a = 18

if a = 18 ,put in eq.(1)

→ b = 18 - 6

→ b = 12

therefore

Side of square (1) is 18 m and side of square (2) is 12 m.

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