Question

7. The first, third, and fourth term of a proportion are 21, 48 and 256 respectively. Find the second
term.​

Answer 1

Question:-

The first, third, and fourth term of a proportion are 21, 48 and 256 respectively. Find the second term.

Answer:-

• The second term is 112.

To find:-

• Second term

Solution:-

• First term = 21
• Third term = 48
• Fourth term = 256

Let,

• Second term = x

According to question,

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: \: \: \: 21 : x : : 48 : 256}$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: \: \: \: \frac{21}{x} = \frac{48}{256} }$

After cross multiplication,

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: \: \: \: 48 \times x = 21 \times 256}$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{21 \times 256}{48} }$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: \: \: \: x = 112}$

Hence,

The second term is 112.

Answer 2

GiveN:-

The first, third, and fourth term of a proportion are 21, 48 and 256 respectively.

To FinD:-

Find the second term.

SolutioN:-

We know in proportion,

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

where,

• a is first term = 21
• b is second term = ?
• c is third term = 48
• d is fourth term = 256

Putting the values,

$\large\implies{\sf{\dfrac{21}{b}=\dfrac{48}{256}}}$

By cross multiplying,

$\large\implies{\sf{21\times256=48\times\:b}}$

$\large\implies{\sf{5376=48b}}$

$\large\implies{\sf{\dfrac{5376}{48}=b}}$

$\large\implies{\sf{\dfrac{\cancel{5376}}{\cancel{48}}=b}}$

$\large\implies{\sf{112=b}}$

$\large\therefore\boxed{\bf{b=112.}}$

VerificatioN:-

$\large\implies{\sf{\dfrac{21}{112}=\dfrac{48}{256}}}$

By cross multiplying,

$\large\implies{\sf{21\times256=48\times112}}$

$\large\implies{\sf{5376=5376}}$

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

• Hence verified.

The second term is 112.