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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

Respuesta :

Answer:

The ratio of x is [tex]\implies x=  \frac{25}{18} y[/tex]

Step-by-step 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 = [tex]\frac{25}{100} \times 40 = 10[/tex]

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 = [tex]\frac{10}{100} \times 40x  = 4x [/tex]

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

and 36 x  = 50 y

[tex]\implies x= \frac{50}{36}  y = \frac{25}{18} y[/tex]

Hence, the ratio of x is [tex]\implies x=  \frac{25}{18} y[/tex]

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