Question

The length and breadth of a rectangle are (a + 5b) units and (7a - b) units respectively. The
perimeter of this rectangle is equal to the perimeter of a square. Find how much is the area of the rectangle less than thatof the square?

​

Answer 1

Answer:

-9a² + 26ab -6b²

Step-by-step explanation:

Length of rectangle: a + 5b

The breadth of rectangle: 7a - b

Perimeter: 2 (l + b)

2 (a + 5b + 7a - b)

2 (8a + 4b)

16a + 8b

Let side of square be x

4x = 16a + 8b

x = 4a + 2b

Area of square: (side)²

(4a + b)²

16a² + b² + 8ab

Area of rectangle: (a + 5b)(7a - b)

7a² - ab + 35ab - 5b²

7a² + 34ab - 5b²

Difference between the area of the rectangle to the square

7a² + 34ab - 5b² - (16a² + b² + 8ab)

7a² + 34ab - 5b² - 16a² - b² - 8ab

-9a² + 26ab -6b²

Thanks. Hope you liked it. If yes, please mark as brainliest. Stay safe!