A uniform iron bar of length 7 m weighs 22.4 kg. How much does the same bar of length 13 m weigh ?

Given:

Weight of 7 m iron bar = 22.4 kg

Weight of 13 m iron bar = ?

Let the weight of 13 m iron bar = x kg

Ratio of lengths : Ratio of weights

7 : 13 :: 22.4 : x

By the rule: Product of Extremes = Product of Means:

7 × x = 13 × 22.4

⇒ x = $\dfrac{13 \times 22.4}{7}$

⇒ x = 13 x 3.2

⇒ x = 41.6

Hence, the bar of length 13 m weighs 41.6 kg.