Question

The heights of three Russian dolls are in the ratio 7: 12: 17. Rewrite this as an equivalent ratio of the form 1: m:n. Give any decimals in your answer to 2 d.p.​

Answer 1

Answer:

7 : 12 : 17 = 1 : 12/7 : 17/7 = 1 : 1.71 : 2.43

Answer 2

Answer:

$1 : 1.71 : 2.43$

Step-by-step explanation:

Let the heights of the Russian dolls be represented by the values $7x$, $12x$, and $17x$, where $x$ is a positive constant.

The given ratio is 7:12:17, which can be expressed as $7x:12x:17x$.

Now, we want to rewrite this ratio in the form 1: $m$: $n$. To do this, we need to find a common factor for $7x$, $12x$, and $17x$.

The common factor is $x$. Divide each term by $x$:

$\dfrac{7x}{x} : \dfrac{12x}{x} : \dfrac{17x}{x}$

Simplify:

$7:12:17$

Now, the equivalent ratio in the form 1: $m$: $n$ is obtained by dividing each term by the smallest term, which is 7:

$\dfrac{7}{7} : \dfrac{12}{7} : \dfrac{17}{7}$

Simplify:

$1 : \dfrac{12}{7} : \dfrac{17}{7}$

As decimals (rounded to 2 decimal places):

$1 : 1.71 : 2.43$

So, the equivalent ratio is:

$\Large\boxed{\boxed{1:1.71:2.43}}$.