Pythagorean theorem - math word problems - page 11 of 68
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:c2 = a2 + b2
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 c2 = a2 + b2, 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: 1341
- Euclidean distance
Calculate the Euclidean distance between shops A, B, and C, where: A 45 0.05 B 60 0.05 C 52 0.09 The first figure is the weight in grams of bread, and the second figure is the USD price. - Medians
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 25 cm and tb=30 cm. - R triangle
Calculate the right triangle area whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg. - Ladder
Ladder 8 m long is leaning against the wall. Its foot is 1 m away from the wall. At which height does the ladder touch the wall?
- Rectangle 79084
A rectangle whose one side measures 35m and the other is 7m shorter than the diagonal of the rectangle. Calculate the content in m². - Calculate 78714
Calculate the size of the base and side of an isosceles triangle if the side is 1 cm longer than the base and the height to the base is 2 cm shorter than the side. - Rectangular 63094
Calculate the perimeter and the area of a rectangular garden if the diagonal length is 18 m long and one of the sides of the garden is 9m long. - Cross-section 5567
What diameter must the trunk of a tree have to carve a beam with a square cross-section of 20 cm on it? - Centimeters 4404
Calculate the diagonal of a square if its area is equal to 169 square centimeters.
- Diagonals
A diagonal of a rhombus is 20 cm long. If its side is 26 cm, find the length of the other diagonal. - Parallelogram 3567
One side of the parallelogram is 5 cm. Can it have 3 cm and 6 cm diagonals? - Calculate 3561
There is a 12 cm long chord in a circle with a radius of 10 cm. Calculate the distance of the chord from the center of the circle. - Circumscribed 3132
The right triangle has squares in the ratio of 5:12, and the circumscribed circle diameter is 26 cm. Determine its perimeter. - Isosceles triangle
Calculate the height of the isosceles triangle ABC with the base AB, AB = c = 10 cm, and the arms a = b = 13 cm long.
- Right triangle
A circle with a radius of 5 cm is described in a right triangle with a 6 cm leg. What is the height at the hypotenuse of this triangle? - Isosceles trapezoid
Find the area of an isosceles trapezoid; if the bases are 12 cm and 20 cm, the arm's length is 16 cm. - Difference of legs
In a right triangle, the hypotenuse length is 65 m, and the difference between legs is 23 m. Calculate the perimeter of this triangle. - Median in right triangle
In the rectangular triangle, ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse). - Waste
How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
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