Question

The first, second and fourth terms of a proportion are 16, 24 and 54 respectively. Then the third term is:​

Answer 1

GiveN:-

The first, second and fourth terms of a proportion are 16, 24 and 54 respectively.

To FinD:-

The third term.

SolutioN:-

In proportion,

$\large\boxed{\bf{\dfrac{a}{b}=\dfrac{c}{d}}}$

where,

• a is the first proportion
• b is the second proportion
• c is the third proportion
• d is the fourth proportion

Let the third proportion be x.

According to the question,

$\large\implies{\sf{\dfrac{16}{24}=\dfrac{x}{54}}}$

By cross multiplying,

$\large\implies{\sf{54\times16=24\times\:x}}$

$\large\implies{\sf{864=24x}}$

$\large\implies{\sf{\dfrac{864}{24}=x}}$

$\large\implies{\sf{\dfrac{\cancel{864}}{\cancel{24}}=x}}$

$\large\implies{\sf{36=x}}$

$\large\therefore\boxed{\bf{Third\:Proportion=36.}}$

• The third proportion is 36. ★

VerificatioN:-

$\large\implies{\sf{\dfrac{a}{b}=\dfrac{c}{d}}}$

$\large\implies{\sf{\dfrac{16}{24}=\dfrac{36}{54}}}$

By cross multiplying,

$\large\implies{\sf{54\times16=24\times36}}$

$\large\implies{\sf{864=864}}$

$\large\therefore\boxed{\bf{LHS=RHS.}}$

• Hence verified. ✔

The third proportion is 36.