Question

Question was provided via image upload.

Explanation:

Identify the given values

We are given a right-angled triangle \(KLM\) with:

• Hypotenuse \(ML = 7.3\text{ cm}\)
• Leg \(KL = 4.2\text{ cm}\)
• Right angle at vertex \(K\)

Calculate the missing leg length

Using the Pythagorean Theorem:

$$ KM^2 + KL^2 = ML^2 $$

$$ KM^2 + 4.2^2 = 7.3^2 $$

$$ KM^2 + 17.64 = 53.29 $$

$$ KM^2 = 53.29 - 17.64 = 35.65 $$

$$ KM = \sqrt{35.65} \approx 5.97\text{ cm} $$

Calculate the perimeter

The perimeter \(P\) is the sum of all three sides:

$$ P = KL + LM + KM $$

$$ P = 4.2 + 7.3 + 5.97 = 17.47\text{ cm} $$

Compare with options

The calculated perimeter is approximately \(17.5\text{ cm}\).

• Option a: \(12.6\text{ cm}\)
• Option b: \(16.3\text{ cm}\)
• Option c: \(17.5\text{ cm}\)
• Option d: \(21.0\text{ cm}\)

The closest value is \(17.5\text{ cm}\).

Answer:

• a. 12.6 cm
• b. 16.3 cm
• c. 17.5 cm (Correct answer)
• d. 21.0 cm