Question

The area of an exhibition hall is 96 sq.m. If the length and breadth be increased by 1 m each, the area
increases by 21 sq.m. Find the length and breadth of the hall.(Solve by using linear equation in 2 variables only..If u need bainliest)​

Answer 1

Answer:

Let length and breadth be x and y .

Given

$xy = 96 \: \: \: \: - - - - - -- eq1 \\ (x + 1)(y + 1) = 96 + 21 \\ xy + x + y + 1 = 117 \\ use \: \: \: \: eq1\\ x + y = 20 - - - - - eq2 \\ again \: from \: \: eq1 \: \: y = \frac{96}{x} \\ \\ x + \frac{96}{x} = 20 \\ {x}^{2} + 96 = 20x \\ {x}^{2} - 20x + 96 = 0 \\ {x}^{2} - 12x - 8x + 96 = 0 \\ (x - 12)(x - 8) = 0 \\ \: \: \: \: \: \: x = 12 \: \: then \: \: y = 8 \: \: \\ or \: \: x = 8 \: \: then \: \: y = 12$