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One of the legs of a right triangle measures 12cm and the other leg measures 16cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth. Answer: cm

One of the legs of a right triangle measures 12 cm 12 \mathrm{~cm} and the other leg measures 16 cm 16 \mathrm{~cm} . Find the measure of the hypotenuse. If necessary, round to the nearest tenth.\newlineAnswer: □\square cm \mathrm{cm}

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Full solution

Q. One of the legs of a right triangle measures 12 cm 12 \mathrm{~cm} and the other leg measures 16 cm 16 \mathrm{~cm} . Find the measure of the hypotenuse. If necessary, round to the nearest tenth.\newlineAnswer: □\square cm \mathrm{cm}
  1. Identify legs and relationship: Identify the legs of the right triangle and the relationship between the legs and the hypotenuse.\newlineThe legs of the right triangle are given as 12 cm12\,\text{cm} and 16 cm16\,\text{cm}. According to the Pythagorean Theorem, the square of the hypotenuse (cc) is equal to the sum of the squares of the other two sides (aa and bb).\newlineMathematically, this is represented as a2+b2=c2a^2 + b^2 = c^2.
  2. Substitute values into theorem: Substitute the given values into the Pythagorean Theorem.\newlineWe have a=12 cma = 12\,\text{cm} and b=16 cmb = 16\,\text{cm}. Plugging these values into the equation, we get:\newline122+162=c212^2 + 16^2 = c^2.
  3. Calculate squares of measurements: Calculate the squares of the given leg measurements. 122=14412^2 = 144 and 162=25616^2 = 256. Now, add these two values to find the square of the hypotenuse. 144+256=c2144 + 256 = c^2.
  4. Add results for hypotenuse: Add the results to find the square of the hypotenuse. 144+256=400=c2144 + 256 = 400 = c^2.
  5. Take square root to solve: Take the square root of both sides of the equation to solve for cc.400=c2\sqrt{400} = \sqrt{c^2}.c=20c = 20.
  6. Check for rounding: Since the problem asks for the hypotenuse to be rounded to the nearest tenth if necessary, we check our answer.\newlineThe hypotenuse is exactly 20 cm20\,\text{cm}, so no rounding is necessary.

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