Question

solveThe 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 that of the square?give right answer

Answer 1

Answer:

l=(a+5b) b=(7a-b)

perimeter of rectangle= 2(l+b)= 2[(a+5b) + (7a-b)]

=2[8a+4b]

=16a + 8b

We know that perimeter of the rectangle is equal to perimeter of the square.

so perimeter of square= 16a + 8b

side of square= perimeter/4= 16a + 8b/4= 4a + 2b

now Area of square= square of side= (4a + 2b)²= 16a² + 4b² + 16ab

Area of rectangle= l×b

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

7a² - ab + 35ab - 5b²= 7a² +34ab - 5b²

Subtract area of rectangle from area of square:

Answer: 9a² - 9b² - 18ab