s. The length of one leg of a right triangle is 5 centimeters shorter than the hypotenuse. The hypotenuse is 15 centimeters. What is the length of the unknown leg of the right triangle rounded to the nearest tenth?

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UpStudy AI · Accepted Answer

**Step 1: Identify the known values**  
The hypotenuse is given as $$15$$ centimeters. One leg is $$5$$ centimeters shorter than the hypotenuse, so that leg is  
$$
15 - 5 = 10 \text{ cm}.
$$

**Step 2: Apply the Pythagorean theorem**  
For a right triangle with legs $$a$$ and $$b$$ and hypotenuse $$c$$, the Pythagorean theorem states:  
$$
a^2 + b^2 = c^2.
$$  
Here, let $$a = 10$$ cm and $$b = x$$ (the unknown leg). Then,  
$$
10^2 + x^2 = 15^2.
$$

**Step 3: Substitute and solve for $$x$$**  
Substitute the given values into the equation:  
$$
100 + x^2 = 225.
$$  
Subtract $$100$$ from both sides to isolate $$x^2$$:  
$$
x^2 = 225 - 100 = 125.
$$  
Taking the square root of both sides:  
$$
x = \sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}.
$$

**Step 4: Approximate the value of $$x$$**  
We know that $$\sqrt{5} \approx 2.236$$. Therefore,  
$$
x \approx 5 \times 2.236 = 11.18.
$$

**Step 5: Round to the nearest tenth**  
Rounded to the nearest tenth, the length of the unknown leg is approximately  
$$
11.2 \text{ centimeters}.
$$
The length of the unknown leg is approximately 11.2 centimeters.

s. The length of one leg of a right triangle is 5 centimeters shorter than the hypotenuse. The hypotenuse is 15 centimeters. What is the length of the unknown leg of the right triangle rounded to the nearest tenth?

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