Question

the perimeter of a rectangle is 8a²+5ab-4b². if length of the rectangle is a²-3ab+4b². Find it's breadth. Also calculate the area of the rectangle ​

Answer 1

GIVEN :-

• Perimeter of rectangle = 8a² + 5ab - 4b².
• Length of rectangle = a² - 3ab + 4b².

TO FIND :-

• The breadth of rectangle.
• Area of rectangle.

SOLUTION :-

☯ Perimeter of rectangle = 2(Length + Breadth)

➬ 8a² + 5ab - 4b² = 2(a² - 3ab + 4b² + Breadth)

➬ 8a² + 5ab - 4b² = 2a² - 6ab + 8b² + 2 breadth

➬ (8a² + 5ab - 4b²) - (2a² - 6ab + 8b²) =2 breadth

➬ 8a² + 5ab - 4b² - 2a² + 6ab - 8b² = 2 breadth

➬ 8a² - 2a² + 5ab + 6ab - 4b² - 8b² = 2 breadth

➬ 6a² + 11ab - 12b² = 2 breadth

➬ breadth = (6a² + 11ab - 12b²)/2

➬ breadth = [(6a²/2) + (11ab/2) - (12b²)/2]

➬ breadth = 3a² + 5.5ab - 6b²

Hence the breadth of rectangle is 3a² + 5.5ab - 6b².

☯ Area of rectangle = Length × breadth

➬ [(a² - 3ab + 4b²)(3a² + 5.5ab - 6b²)]

➬ [a²(3a² + 5.5ab - 6b²) -3ab((3a² + 5.5ab - 6b²) + 4b²((3a² + 5.5ab - 6b²)]

➬ [3a⁴ + 5.5a³b - 6a²b² - 9a³b - 16.5a²b² + 18ab³ + 12a²b² + 22ab³ - 24b⁴

➬ 3a⁴ + 5.5a³b - 9a³b - 6a²b² - 16.5a²b² + 12a²b² + 18ab³ + 22ab³ - 24b⁴.

➬ 3a⁴ - 3.5a³b - 22.5a²b² + 12a²b² + 40ab³ - 24b⁴

➬ 3a⁴ - 3.5a³b - 10.5a²b² + 40ab³ - 24b⁴

Hence area of rectangle is 3a⁴ - 3.5a³b - 10.5a²b² + 40ab³ - 24b⁴.