# Pythagorean theorem

The Pythagorean theorem states: When squares are drawn on the legs of a right triangle, the sum of these areas is equal to the area of the square drawn on the hypotenuse of the same triangle.

**Example 1**

Find *x*

We use Pythagorean theorem

Because it is the length of the hypotenuse, only a positive answer is valid.

**Example 2**

Find *x*

We use Pythagorean theorem

Because it is the length of the leg, only a positive answer is valid.

**Example 3**

Liisa-Petter was thinking of building a slide from her balcony to the parking lot next to her car. She was a pretty lazy person. Liisa-Petter's balcony was 15 meters high and the parking space 45 meters from her house.

How long should the slide be? Give the answer to the nearest tenth of a metre.

First we draw the situation

The slide is the hypotenuse of the formed right triangle. We use Pythagorean theorem to solve this.

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