# Pythagorean theorem - practice problems

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:c

^{2}= a

^{2}+ b

^{2}

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

A common proof of the Pythagorean Theorem is called the "area proof". To prove the theorem using this method, we can create a square with side length c and two smaller squares with side lengths a and b, as shown in the figure. We can then place the smaller squares next to each other to form a rectangle with area a x b. We can then see that the area of the square with side length c is equal to the sum of the areas of the smaller squares, which is equal to the area of the rectangle. This demonstrates that c

^{2}= a

^{2}+ b

^{2}, as stated in the theorem.

Another proof is Euclidean proof which is based on the Euclidean geometry and construction of a line segment that is c and perpendicular to the line segment of a and b.

#### Number of problems found: 1239

- Square

Calculate the side of a square with a diagonal measurement of 10 cm. - Laws

From which law directly follows the validity of Pythagoras' theorem in the right triangle? ... - ABS CN

Calculate the absolute value of the complex number -15-29i. - Triangle

Can an equilateral triangle have a right angle? - Calculate

Calculate the length of a side of the equilateral triangle with an area of 50cm². - Square

Calculate the area of the square with diagonal 64 cm. - Equilateral triangle

Find the area of an equilateral triangle with a side of 15 cm. - Euclid2

The ABC right triangle with a right angle at C is side a=29 and height v=17. Calculate the perimeter of the triangle. - Isosceles IV

In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle. - RT and circles

Solve the right triangle if the radius of the inscribed circle is r=9 and the radius of the circumscribed circle is R=23. - Catheti

The hypotenuse of a right triangle is 41, and the sum of legs is 49. Calculate the length of its legs. - How long

How long is the diagonal of the square with side a = 50mm? - Bridge

The bridge arc has a span of 72 m and height 5 m. Calculate the radius of the circle arc of this bridge. - Height

Calculate the height of the equilateral triangle if its perimeter is 8. - Triangle 36091

Decide if the triangle is right (sides 5,11,7, cm) - Isosceles triangle

Calculate the area of an isosceles triangle, the base measuring 16 cm and the arms 10 cm. - Is right triangle

Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m - Circumference 47983

What is the area of an equilateral triangle with a circumference of 63 cm? - The diagonal 4

The diagonal of a rhombus measures 16cm and 30cm. Find its perimeter. - One leg

One leg of a right triangle is 1 foot longer than the other leg. The hypotenuse is 5 feet. Find the lengths of the three sides of the triangle.

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