Question

61

P is a rectangle with length 40 cm and width x cm.
Q is a rectangle with width y cm.
The length of Q is 25% more than the length of P.
The area of Q is 10% less than the area of P.
Work out the ratio x:
Give your answer in its simplest form.
x cm
40 cm
y cm

Answer 1

The ratio of x is
`\implies x=  (25)/(18) y`

Explanation:

The dimensions of P rectangle:

Length = 40 cm , Width = x cm

The dimensions of Q rectangle:

Length = 25% more than Length of P , Width = y cm

Now, 25% of 40 =
`(25)/(100) * 40 = 10`

So, the length of Rectangle Q = 40 + 10 = 50 cm

AREA OF RECTANGLE = LENGTH x WIDTH

So, Area of Rectangle P = 40(x) = 40 x

and Area of Rectangle Q = 50(y) = 50 y

Now, Area of Q is 10% less than the area of P

10% of area of P =
`(10)/(100) * 40x  = 4x`

So, the area of Q = 40- 4x = 36 x

and 36 x = 50 y

`\implies x= (50)/(36)  y = (25)/(18) y`

Hence, the ratio of x is
`\implies x=  (25)/(18) y`