How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

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Geometry › How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

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A right triangle has legs of 15m and 20m. What is the length of the hypotenuse?

30m

45m

35m

40m

25m

CORRECT

Explanation

The Pythagorean theorem is a2 + b2 = c2, where a and b are legs of the right triangle, and c is the hypotenuse.

(15)2 + (20)2 = c2 so c2 = 625. Take the square root to get c = 25m

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In the figure above, is a square and is three times the length of . What is the area of ?

CORRECT

Explanation

Assigning the length of ED the value of x, the value of AE will be 3_x_. That makes the entire side AD equal to 4_x_. Since the figure is a square, all four sides will be equal to 4_x_. Also, since the figure is a square, then angle A of triangle ABE is a right angle. That gives triangle ABE sides of 3_x_, 4_x_ and 10. Using the Pythagorean theorem:

(3_x_)2 + (4_x_)2 = 102

9_x_2 + 16_x_2 = 100

25_x_2 = 100

_x_2 = 4

x = 2

With x = 2, each side of the square is 4_x_, or 8. The area of a square is length times width. In this case, that's 8 * 8, which is 64.

What is the hypotenuse of a right triangle with side lengths and ?

CORRECT

Explanation

The Pythagorean Theorem states that . This question gives us the values of and , and asks us to solve for .

Take and and plug them into the equation as and :

$12^{2}+16^{2}=c^{2}$

Now we can start solving for :

$144+256=c^{2}$

$400=c^{2}$

$\sqrt{400}=\sqrt{c^{2}}$

The length of the hypotenuse is .

Find the length of the hypotenuse.

$\sqrt{14}$

CORRECT

$4\sqrt2$

$\sqrt{15}$

$3\sqrt3$

Explanation

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

Substitute in the given values.

$c^2=(\sqrt6)^2+(2\sqrt2)^2$

Simplify.

Solve.

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=c=\sqrt{14}$

In order to get to work, Jeff leaves home and drives 4 miles due north, then 3 miles due east, followed by 6 miles due north and, finally, 7 miles due east. What is the straight line distance from Jeff’s work to his home?

2√5

10√2

CORRECT

6√2

Explanation

Jeff drives a total of 10 miles north and 10 miles east. Using the Pythagorean theorem (a2+b2=c2), the direct route from Jeff’s home to his work can be calculated. 102+102=c2. 200=c2. √200=c. √100√2=c. 10√2=c

Find the length of the hypotenuse.

CORRECT

$6\sqrt{85}$

$12\sqrt{85}$

Explanation

Use the Pythagorean Theorem to find the length of the hypotenuse, .

$c=\sqrt{a^2+b^2}$

Substitute in the values for the legs, $a \text{ and }b$ , to find the length of the hypotenuse.

$c=\sqrt{6^2+(\sqrt{85})^2}$

Simplify.

$c=\sqrt{121}$

Solve.

Trig_id

If and , how long is side ?

CORRECT

Not enough information to solve

Explanation

This problem is solved using the Pythagorean theorem $(a^{2}+b^{2}=c^{2})$ . In this formula and are the legs of the right triangle while is the hypotenuse.