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Flashcards: Understand right triangles

Find the length of the hypotenuse of a right triangle whose legs are the following lengths:

$a=3 \textup{ and }b=5$ $\displaystyle a=3 \textup{ and }b=5$

5.83 $\displaystyle 5.83$

$\displaystyle 7$

8.53 $\displaystyle 8.53$

$\displaystyle 4$

3.85 $\displaystyle 3.85$

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Flashcards: Understand right triangles

Find the length of the hypotenuse of a right triangle whose legs are the following lengths:

$a=3 \textup{ and }b=5$ $\displaystyle a=3 \textup{ and }b=5$

5.83 $\displaystyle 5.83$

$\displaystyle 7$

8.53 $\displaystyle 8.53$

$\displaystyle 4$

3.85 $\displaystyle 3.85$

Report an Error Copyright Notice

Flashcards: Understand right triangles

Find the length of the hypotenuse of a right triangle whose legs are the following lengths:

$a=3 \textup{ and }b=5$ $\displaystyle a=3 \textup{ and }b=5$

Your answer:

$\displaystyle 7$

Your answer:

8.53 $\displaystyle 8.53$

Your answer:

$\displaystyle 4$

Your answer:

3.85 $\displaystyle 3.85$

Correct answer:

5.83 $\displaystyle 5.83$

Explanation:

The hypotenuse of a right triangle can be calculated using the Pythagorean Theorem. This theorem states that if we know the lengths of the two other legs of the triangle, then we can calculate the hypotenuse. It is written in the following way:

$\displaystyle a^2+b^2=c^2$

In this formula the legs are noted by the variables, $\displaystyle a$ and $\displaystyle b$ . The variable $\displaystyle c$ represents the hypotenuse.

Substitute and solve for the hypotenuse.

$\displaystyle 3^2+5^2=c^2$

Simplify.

$\displaystyle 9+25=c^2$

34=c^2 $\displaystyle 34=c^2$

Take the square root of both sides of the equation.

$\sqrt{c^2}=\sqrt{34}$ $\displaystyle \sqrt{c^2}=\sqrt{34}$

c=5.83 $\displaystyle c=5.83$

Flashcards: Understand right triangles

If the two legs of a right triangle are $\displaystyle 10$ cm and $\displaystyle 15$ cm, what is the length of the hypotenuse. Answer must be in SIMPLIFIED form (or lowest terms).

$5\sqrt{11}$ $\displaystyle 5\sqrt{11}$ cm

$5\sqrt{13}$ $\displaystyle 5\sqrt{13}$ cm

18.03 $\displaystyle 18.03$ cm

$5\sqrt{17}$ $\displaystyle 5\sqrt{17}$ cm

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Flashcards: Understand right triangles

If the two legs of a right triangle are $\displaystyle 10$ cm and $\displaystyle 15$ cm, what is the length of the hypotenuse. Answer must be in SIMPLIFIED form (or lowest terms).

Your answer:

$5\sqrt{11}$ $\displaystyle 5\sqrt{11}$ cm

Your answer:

18.03 $\displaystyle 18.03$ cm

Your answer:

$5\sqrt{17}$ $\displaystyle 5\sqrt{17}$ cm

Correct answer:

$5\sqrt{13}$ $\displaystyle 5\sqrt{13}$ cm

Explanation:

Step 1: Recall the Pythagorean theorem statement and formula.

Statement: For any right triangle, the sums of the squares of the shorter sides is equal to the square of the longest side.

Formula: In a right triangle ABC $\displaystyle ABC$ , If a,b $\displaystyle a,b$ are the shorter sides and $\displaystyle c$ is the longest side.. then,

$\displaystyle a^2+b^2=c^2$

Step 2: Plug in the values given to us in the problem....

$\displaystyle (10)^2+(15)^2=c^2$

Evaluate:

$(10\times 10)+(15\times 15)=c^2$ $\displaystyle (10\times 10)+(15\times 15)=c^2$

Simplify:

$\displaystyle 100+225=c^2$

Simplify:

325=c^2 $\displaystyle 325=c^2$

Take the square root...

$\sqrt{325}=c$ $\displaystyle \sqrt{325}=c$

Step 3: Simplify the root...

$\sqrt {325}=\sqrt {25\times13}=\sqrt{5\times 5\times 13}=5\sqrt {13}$ $\displaystyle \sqrt {325}=\sqrt {25\times13}=\sqrt{5\times 5\times 13}=5\sqrt {13}$

The length of the hypotenuse in most simplified form is $5\sqrt{13}$ $\displaystyle 5\sqrt{13}$ cm.

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Flashcards: Understand right triangles

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