Question

1. a right triangle has leg length of 4 inches and 5 inches. what is the length of the hypotenuse? write the answer as a square root and round to the nearest tenth of an inch.

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle with legs $a$ and $b$, hypotenuse $c$ is $c=\sqrt{a^2+b^2}$. Substitute $a=4$, $b=5$.
$$c=\sqrt{4^2+5^2}$$

Step2: Calculate squared terms

Compute $4^2$ and $5^2$, then sum.
$$c=\sqrt{16+25}=\sqrt{41}$$

Step3: Round to nearest tenth

Calculate decimal value of $\sqrt{41}\approx6.403$, round to 1 decimal place.
$$\sqrt{41}\approx6.4$$

Answer:

As a square root: $\sqrt{41}$ inches
Rounded to the nearest tenth: 6.4 inches