# Quadratic equation + right triangle - math problems

- A rectangle 2

A rectangle has a diagonal length of 74cm. It’s sides are 5:3. Find its lengths. - Sides of right angled triangle

One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - Secret treasure

Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure. - Medians in right triangle

It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides? - Faces diagonals

If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.2, y=1.7, z=1.45 - Two chords

Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle. - Trapezoid MO

The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Cuboid

Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm^{3}. Calculate the length of the other edges. - Right triangle Alef

The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs. - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ? - Right triangle

Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle. - R triangle

Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg. - Tangents

To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre. - Euclid1

Right triangle has hypotenuse c = 27 cm. How large sections cuts height h_{c}=3 cm on the hypotenuse c? - Hypotenuse and height

In a right triangle is length of the hypotenuse c = 56 cm and height h_{c}= 4 cm. Determine the length of both trangle legs. - RT - hypotenuse and altitude

Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments? - Perimeter and legs

Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm^{2}. - Sphere and cone

Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone? - Euclid3

Calculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg c_{b}= 39 cm. - Column

Perpendicular pole high 8 m tall broke and its toe fell 2.7 m from the bottom of the pole. At what height above the ground pole broke?

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