Question

the perimeter of a square and a rectangle are equal. The length of the rectangle is 11cm and area of the square is 4cm^2 more than the area of the rectangle.find the side of the square?

Answer 1

Given data : The perimeter of a square and a rectangle are equal. The length of the rectangle is 11 cm and area of the square is 4cm² more than the area of the rectangle.

To find : The side of square ?

Solution : Now according to given,

• Length of rectangle = 11 cm

Now, by formula of area's of square and rectangle and according to given ;

Let, side of square be x,

⟹ perimeter of square = perimeter of rectangle

⟹ 4 * x = 2 * (length + breadth)

⟹ 4 * x = 2 * (11 + breadth)

⟹ 2 * x = 11 + breadth

⟹ breadth = 2x - 11 ----[ 1 ]

⟹ Area of square = Area of rectangle + 4 cm²

⟹ x² = (length * breadth) + 4

⟹ x ² - 4 = 11 * breadth

⟹ breadth = {x² - 4}/11 ----[ 2 ]

Now, from eq. [ 1 ] and eq. [ 2 ]

⟹ 2x - 11 = {x² - 4}/11

⟹2x = {x² - 4}/11 + 11

⟹ 2x = {x² - 4 + 121}/11

⟹ 11 * {2x} = x² - 4 + 121

⟹ 22x = x² - 4 + 121

⟹ 22x = x² + 117

⟹ x² - 22x + 117 = 0

Now, comparing above eq. with ax² + bx + c = 0

where,

• a = 1
• b = - 22
• c = 117

Now, by formula ;

⟹ x = {- b ± √[b² - 4ac]}/2a

⟹ x = {- (-22) ± √[(-22)² - 4 * 1 * 117]}/2*1

⟹ x = { 22 ± √[484 - 468]}/2

⟹ x = {22 ± √16}/2

⟹ x = {22 ± 4}/2

⟹ x = {22 + 4}/2 or x = {22 - 4}/2

⟹ x = 26/2 or x = 18/2

⟹ x = 13 cm or x = 9 cm

Answer : Hence, the side of square is 13 cm or 9 cm.

Answer 2

Answer:

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