### Example question #1 : exactly how To find The size Of The Hypotenuse of A best Triangle : Pythagorean to organize

If

and , just how long is side ?Explanation:

This trouble is addressed using the Pythagorean theorem

. In this formula and are the legs of the ideal triangle while is the hypotenuse.You are watching: How does the length of the hypotenuse relate to the length of the legs

Using the labels of our triangle us have:

### Example concern #1 : how To discover The length Of The Hypotenuse the A ideal Triangle : Pythagorean theorem

Explanation:

Therefore *h*2 = 50, therefore *h* = √50 = √2 * √25 or 5√2.

### Example concern #3 : just how To find The length Of The Hypotenuse that A ideal Triangle : Pythagorean to organize

The elevation of a right circular cylinder is 10 inches and the diameter that its base is 6 inches. What is the street from a allude on the sheet of the base to the center of the entire cylinder?

Explanation:

The best thing to do below is to attract diagram and draw the appropiate triangle because that what is gift asked. It does not matter where you location your suggest on the base because any point will produce the exact same result. We know that the center of the basic of the cylinder is 3 inches away from the base (6/2). We also know the the facility of the cylinder is 5 inches from the basic of the cylinder (10/2). So we have actually a right triangle with a elevation of 5 inches and a base of 3 inches. So making use of the Pythagorean organize 32 + 52 = c2. 34 = c2, c = √(34).

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### Example question #4 : exactly how To find The size Of The Hypotenuse of A right Triangle : Pythagorean organize

A appropriate triangle with sides A, B, C and also respective angle a, b, c has actually the adhering to measurements.

Side A = 3in. Side B = 4in. What is the size of next C?

**Possible Answers:**

6

7

25

9

5

**Correct answer:**

5

Explanation:

The correct answer is 5. The pythagorean theorem claims that a2 + b2 = c2. For this reason in this situation 32 + 42 = C2. Therefore C2 = 25 and C = 5. This is additionally an example of the usual 3-4-5 triangle.

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### Example inquiry #5 : just how To uncover The length Of The Hypotenuse that A ideal Triangle : Pythagorean theorem

The lengths of the three sides of a ideal triangle type a collection of consecutive also integers once arranged from least to greatest. If the second largest side has actually a length of x, climate which that the following equations might be supplied to fix for x?

**Possible Answers:**

(x – 1)2 + x2 = (x + 1)2

(x – 2)2 + x2 = (x + 2)2

(x – 2) + x = (x + 2)

x 2 + (x + 2)2 = (x + 4)2

(x + 2)2 + (x – 2)2 = x2

**Correct answer:**

(x – 2)2 + x2 = (x + 2)2

Explanation:

We are told that the lengths kind a collection of consecutive even integers. Due to the fact that even integers are two devices apart, the side lengths have to differ by two. In other words, the biggest side size is two higher than the second largest, and also the second largest size is two higher than the smallest length.

The 2nd largest size is same to x. The second largest size must thus be two less than the biggest length. We can represent the largest length together x + 2.

Similarly, the second largest length is two larger than the the smallest length, i m sorry we can thus stand for as x – 2.

To summarize, the lengths of the triangle (in regards to x) room x – 2, x, and x + 2.

In stimulate to solve for x, we can exploit the fact that the triangle is a appropriate triangle. If we apply the Pythagorean Theorem, us can set up one equation that can be offered to solve for x. The Pythagorean Theorem says that if a and b space the lengths the the legs of the triangle, and also c is the length of the hypotenuse, then the complying with is true:

a2 + b2 = c2

In this certain case, the 2 legs of ours triangle are x – 2 and x, because the legs room the two smallest sides; therefore, we deserve to say that a = x – 2, and also b = x. Lastly, we have the right to say c = x + 2, since x + 2 is the size of the hypotenuse. Subsituting these worths for a, b, and c into the Pythagorean Theorem yields the following: