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A right triangle and two of its side lengths are shown in the diagram.

\[ 39 \, \text{cm} \]
\[ 12 \, \text{cm} \]
\[ x \, \text{cm} \]

Which measurement is closest to the value of \( x \) in centimeters?

A. 37.1 cm
B. 51 cm
C. 27 cm
D. 40.8 cm

Answer :

The measurement closest to the value of x is 40.8 cm. So the answer is D: 40.8 cm.

Let's solve for the missing side length of the right triangle.

Given:

Right triangle with one right angle at vertex A

Side length AC = 39 cm

Side length BC = 12 cm

We're asked to find the missing side length, which we'll call AB. We can use the Pythagorean theorem to solve for AB:

Pythagorean theorem: In a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is AB, and the other two sides are AC and BC. So we can write:

AB² = AC² + BC²

Substituting in the given values:

AB² = 39² + 12²

AB² = 1521 + 144

AB² = 1665

Taking the square root of both sides to solve for AB:

AB = √1665

Rounding to the nearest centimeter:

AB ≈ 40.8 cm

Therefore, the measurement closest to the value of x is 40.8 cm. So the answer is D: 40.8 cm.

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Rewritten by : Barada

Answer:

Hey Army! The correct answer would be A. 37.1cm

Step-by-step explanation:

I got this correct on my test :)

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