Problem 18: A trader paid import duty of 38 kobo in the naira on the cost of an engine. If a total of $N22,800.00$ was paid as import duty, calculate the cost of the engine. Problem 19: The height of an equilateral triangle is $10\sqrt{3}$ cm. Calculate its perimeter.

1. Problem Description

Problem 18: A trader paid import duty of 38 kobo in the naira on the cost of an engine. If a total of $N22,800.00$ was paid as import duty, calculate the cost of the engine.

Problem 19: The height of an equilateral triangle is $10\sqrt{3}$ cm. Calculate its perimeter.

2. Solution Steps

Problem 18:

We know that 1 naira = 100 kobo. The import duty is 38 kobo in the naira, which means for every 100 kobo (N1) of the engine cost, the import duty is 38 kobo (N0.38).

Let $x$ be the cost of the engine in naira. The import duty is $0.38x$.

We are given that the total import duty is N22,

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0

0. So, we have the equation $0.38x = 22800$.

Dividing both sides by 0.38 gives $x = \frac{22800}{0.38} = \frac{2280000}{38} = 60000$.

Therefore, the cost of the engine is N60,

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0.

Problem 19:

Let the side length of the equilateral triangle be $s$.

The height of an equilateral triangle is given by the formula $h = \frac{s\sqrt{3}}{2}$.

We are given that $h = 10\sqrt{3}$ cm.

Therefore, $10\sqrt{3} = \frac{s\sqrt{3}}{2}$.

Multiplying both sides by 2, we get $20\sqrt{3} = s\sqrt{3}$.

Dividing both sides by $\sqrt{3}$, we get $s = 20$ cm.

The perimeter of an equilateral triangle is $3s$.

So the perimeter is $3(20) = 60$ cm.

3. Final Answer

Problem 18: A. N60,000.00

Problem 19: B. 60 cm