Question

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Explanation:

Identify given values

We have a rectangular carpet.
Length \(l = 7\text{ ft}\).
Diagonal \(d = \sqrt{74}\text{ ft}\).

Find the width

Using the Pythagorean Theorem:

$$ l^2 + w^2 = d^2 $$

Substitute the values:

$$ 7^2 + w^2 = (\sqrt{74})^2 $$

$$ 49 + w^2 = 74 $$

$$ w^2 = 25 $$

$$ w = 5\text{ ft} $$

Calculate the perimeter

Using the perimeter formula:

$$ P = 2(l + w) $$

$$ P = 2(7 + 5) = 24\text{ ft} $$

Calculate the area

Using the area formula:

$$ A = l \times w $$

$$ A = 7 \times 5 = 35\text{ sq ft} $$

Match the options

The perimeter is \(24\text{ ft}\) and the area is \(35\text{ square feet}\).
This matches option (b).

Answer:

• a) Perimeter 42 square feet, Area 45 square feet
• b) Perimeter 24, Area 35 square feet (Correct answer)
• c) The Perimeter cannot be found
• d) The Area cannot be found