Question

If x, y and z are in continued proportion then $z:x::z^2:y^2$.

Continued proportion means a:b : : b:c

• A. True
• B. False

Answer 1

The correct option is A

True

Three numbers 'a', 'b' and 'c' are said to be continued proportion if a, b and c are in proportion. Thus, if a, b and c are in continued proportion, then a, b, b, c are in proportion i.e. a : b : : b : c.

So, $\frac{a}{b}=\frac{b}{c}$

If x, y, and z are in continued proportion then $y^2=xz$
Multiply both sides of the equation by $z$
equation becomes, $z{y}^2=x{z}^2$
$⟹$ $\left(z/x\right)=\left(z^2/y^2\right)$
$⟹$ $z:x::z^2:y^2$