Question

17. This length of three ribbons is in the ratio 7:5:9. If the sum of the lengths of
the three ribbons are 42 cm, find the length of the smallest ribbon​

Answer 1

Answer :-

• The length of the smallest ribbon = 10 cm.

Given :-

• The length of three ribbons is in the ratio 7 : 5 : 9.
• The sum of the lengths of the three ribbons is 42 cm.

To find :-

• The length of the smallest ribbon.

Step-by-step explanation :-

• The lengths of the three ribbons is in the ratio 7 : 5 : 9.

• Therefore, let their lengths be 7x, 5x and 9x respectively.

• Now, the sum of their lengths = 42 cm.

• So, these three lengths must add up to 42 cm.

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Calculations :-

Let's find out answer now!

$\tt \implies 7x + 5x + 9x = 42$

Adding 7x, 5x and 9x,

$\tt \implies 21x = 42$

Transposing 21 from LHS to RHS, changing it's sign,

$\tt \implies x = \dfrac{42}{21}$

Dividing 42 by 21,

$\tt \implies x = 2.$

• The value of x = 2.

So, the lengths of all the ribbons are as follows :-

$\bf 7x = 7 \times 2 = 14 \: cm.$

$\bf 5x = 5 \times 2 = 10 \: cm.$

$\bf 9x = 9 \times 2 = 18 \: cm.$

Now, it is clear that :-

$\underline{\boxed{ \sf10 \: cm \: is \: the \: smallest \: here.}}$

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• Hence, the length of the smallest ribbon = 10 cm.

Answer 2

$\begin{gathered}\begin{gathered}\bf \: Given - \begin{cases} &\sf{length \: of \: ribbons \: is \: 7 : 5 : 9} \\ &\sf{sum \: of \: length \: of \:3 \: parts \: is \: 42 \: cm } \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To\:find - \begin{cases} &\sf{length \: of \: smallest \: ribbon}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline{\bold{Solution :- }}$

$\begin{gathered}\begin{gathered}\bf \: Let \: length \: of \: ribbons \: be - \begin{cases} &\sf{7x} \\ &\sf{5x}\\ &\sf{9x} \end{cases}\end{gathered}\end{gathered}$

So,

$\large \underline{\tt \:{ According \: to \: statement }}$

$\rm :\longmapsto\:Sum \: of \: three \: lengths = 42 \: cm$

$\rm :\longmapsto\:7x + 5x + 9x = 42$

$\rm :\longmapsto\:21x = 42$

$\bf\implies \: \boxed{ \bf \: x = 2}$

$\begin{gathered}\begin{gathered}\bf \: Hence, \: length \: of \: ribbons \: are - \begin{cases} &\sf{7x = 14 \: cm} \\ &\sf{5x = 10 \: cm}\\ &\sf{9x = 18 \: cm} \end{cases}\end{gathered}\end{gathered}$

So,

$\begin{gathered}\begin{gathered}\bf \:Smallest \: length \: of \: ribbon \: = \begin{cases} &\sf{10 \: cm}  \end{cases}\end{gathered}\end{gathered}$