Question

tom bought a new mirror for his house. one side of the mirror is 38 inches and the other side is 30 inches.

what is the length of the diagonal of the mirror? answer choices are rounded to the nearest inch.

23 inches
34 inches
68 inches
48 inches

Explanation:

Identify the geometric relationship

Using the Right Triangle Geometry knowledge point
A rectangular mirror with side lengths \(a = 38\text{ inches}\) and \(b = 30\text{ inches}\) forms a right triangle where the diagonal \(c\) is the hypotenuse.

Apply the Pythagorean theorem

Using the Pythagorean Theorem knowledge point

$$ c^2 = a^2 + b^2 $$

$$ c^2 = 38^2 + 30^2 $$

$$ c^2 = 1444 + 900 = 2344 $$

$$ c = \sqrt{2344} \approx 48.4149\text{ inches} $$

Round to the nearest inch

Using the Pythagorean Theorem knowledge point

$$ c \approx 48\text{ inches} $$

Answer:

• 23 inches
• 34 inches
• 68 inches
• 48 inches (Correct answer)