Question

The length, $l$, of an object is inversely proportional to the square of its height, $h$. When the height of that object is 5 units, its length is 4.8 units. What would be the length of the object if its height were reduced by 20% ?

• A. $9.5$ units
• B. $11.75$ units
• C. $7.5$ units

Answer 1

The correct option is C $7.5$ units

Given: At $h=5\text{units},l=4.8\text{units}$

We know that $l\propto \frac{1}{h^2}$

$h^{2}l=k=5^2\times 4.8=120$
If height were reduced by 20%
then new height would be
$5-\frac{20}{100}\times 5=5-1=4$ units

plugging in $h=4\text{in}{h}^{2}l=k=120$
we get,
$l=\frac{120}{4^2}=\frac{120}{16}=7.5\text{units}$