Question

In the angle shown below, as the distance (represented by a,x ) from the vertex of the angle changes, the height (represented by b, h) also changes.

Given that $h\propto x$, find the constant of proportionality.

• A. $\frac{a}{b}$
• B. 1
• C. $\frac{b}{2}$
• D. $\frac{a}{4}$

Answer 1

The correct option is A

$\frac{a}{b}$

Let us consider a point A on the slanted line at a distance of $a$ units from O and $b$ units from the baseline.

Let C be another such point which is $x$ units from O and $h$ units from E.

Then $△OAD\sim △OCE$ (AA similarity)

$⟹\frac{OA}{OC}=\frac{AD}{CE}$

i.e.,$\frac{a}{x}=\frac{b}{h}$

$⟹h=x\times \frac{a}{b}$

$⟹h\propto x$

Thus, the constant of proportionality is $\frac{a}{b}$