Question

A rectangle has length 72 cm and width 56 cm. The other rectangle has the same area as this one, but its width is 21 cm. What is the constant of variation?

Answer 1

The length of the rectangle is = 72 cm

The width of the rectangle is = 56 cm

Area of the rectangle is = $length*width$

= $72\times56=4032$ cm²

As given, the other rectangle has the same area as this one, but its width is 21 cm.

Let the length here be = x

$4032=x*21$

$x=\frac{4032}{21}=192$

Hence, length is 192 cm.

We can see that as width decreases, the length increases if area is constant and when length decreases then width increases if area is constant.

So, in the new rectangle,constant of variation=k is given by,

$\frac{192}{72}=\frac{8}{3}$ or $\frac{56}{21}=\frac{8}{3}$

Hence, the constant of variation is $\frac{8}{3}$