Question

if the first second and third terms of a proportion are 45,6,15 respectively find the fourth term​

Answer 1

Solution :

Given:

• First term = 45.
• Second term = 6.
• Third term = 15.
• Fourth term = Unknown.

Need to find:

• Fourth term = ?

Explanation:

Let us consider the, the fourth term be "k".

Then,

→ 1ˢᵗ term : 2ⁿᵈ term :: 3ʳᵈ term : 4ᵗʰ term

→ 45 : 6 :: 15 : k.

We know that, if we are given with, first term, second term and third term of a proportion, we have the required formula, that is,

• Product of Mean = Product of Outcome.

By using the formula to calculate the fourth term of a proportion and substituting all the given values in the formula, we get:

→ 6 * 15 = 45 * k

→ 90 = 45 * k

→ 90 = 45k

→ 45k = 90

→ k = 90/45

→ k = 2 (Ans.)

Hence, the fourth term of a proportion is 2.

Answer 2

Answer:

Given :-

• The first, second and third terms of a proportional are 45 , 6 , 15 respectively.

To Find :-

• What is the fourth term.

Solution :-

Let, the fourth proportional be x

According to the question,

↦ $\sf 45 : 6 : : 15 : x$

↦ $\sf \dfrac{45}{6} =\: \dfrac{15}{x}$

By doing cross multiplication we get,

↦ $\sf 45 \times x =\: 6 \times 15$

↦ $\sf 45x =\: 90$

↦ $\sf x =\: \dfrac{\cancel{90}}{\cancel{45}}$

➠ $\sf\bold{\red{x =\: 2}}$

$\therefore$ The fourth proportional is 2.

$\rule{300}{2}$

$\sf\boxed{\bold{\pink{VERIFICATION :-}}}$

↦ $\sf 45 : 6 : : 15 : x$

↦$\sf \dfrac{45}{6} =\: \dfrac{15}{x}$

By putting x = 2 we get,

↦ $\sf \dfrac{45}{6} =\: \dfrac{15}{2}$

↦ $\sf 45 \times 2 =\: 6 \times 15$

➠ $\sf\bold{\purple{90 =\: 90}}$

Hence, Verified .