One of the legs of a right triangle measures 10 cm and the other leg measures 14 cm . Find the
measure of the hypotenuse. If necessary, round to the nearest tenth.

Question

One of the legs of a right triangle measures 10 cm and the other leg measures 14 cm . Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

UpStudy AI · Accepted Answer

To find the measure of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Given:
- One leg of the right triangle measures 10 cm.
- The other leg measures 14 cm.

Let's denote the length of the hypotenuse as $$ c $$.

According to the Pythagorean theorem:
$$ a^2 + b^2 = c^2 $$

Substitute the given values:
$$ 10^2 + 14^2 = c^2 $$
$$ 100 + 196 = c^2 $$
$$ 296 = c^2 $$

Now, we need to find the square root of 296 to determine the length of the hypotenuse.

$$ c = \sqrt{296} $$

Let's calculate the value of $$ c $$ and round it to the nearest tenth.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{296}$$
- step1: Write as a product:
  $$\sqrt{4\times 74}$$
- step2: Write in exponential form:
  $$\sqrt{2^{2}\times 74}$$
- step3: Use the properties of radicals:
  $$\sqrt{2^{2}}\times \sqrt{74}$$
- step4: Simplify the root:
  $$2\sqrt{74}$$
The length of the hypotenuse is approximately 17.2 cm when rounded to the nearest tenth.
The hypotenuse is approximately 17.2 cm.

One of the legs of a right triangle measures 10 cm and the other leg measures 14 cm . Find the
measure of the hypotenuse. If necessary, round to the nearest tenth.

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