Question

The sides of a rectangle are in the ratio 4:5
a)By what fraction should the shorter side be increased to make it a square?
b)By what fraction should the larger side be decreased to make it a square​

Answer 1

Answer:

a)let the sides of the rectangle be 4x and 5x

let the required fraction be a/b

$\frac{4x}{5x} + \frac{a}{b } = \frac{5x}{5x} \\ = \frac{4x }{5x } + \frac{a}{b} = 1 \\ \frac{a}{b} = 1 - \frac{4x}{5x} \\ = \frac{5x - 4x}{5x} = \frac{x}{5x} = \frac{1}{5}$

b)now let the sides of the rectangle be 5x and 4x

let the required fraction be a/b

$\frac{a}{b} - \frac{5x}{4x} = \frac{5x}{5x} \\ \frac{a}{b} - \frac{5x}{4x} = 1 \\ \frac{a}{b} = 1 + \frac{5x}{4x} = \frac{4x + 5x}{4x} = \frac{9x}{4x} \\ = \frac{9}{4}$