# Pythagorean theorem - math word problems

- Diagonal

he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal. - Equation of circle 2

Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x. - Pendulum

Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm. - Garden fence

The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced? - Quadrangular pyramid

Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =? - Tangent

What distance is the tangent t of the circle (S, 4 cm) and the chord of this circle, which is 6 cm long and parallel to the tangent t? - Tangent 3

In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm. - Chord

It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB. - Surface area of the top

A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder. - The ladder

The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall? - Is right triangle

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

Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm. - Right angled triangle 2

LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n - Body diagonal

Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base, - The mast

A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance. - Cube wall

The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube. - Perimeter of triangle

In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference. - Diagonal 20

Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be? - Cube wall

Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume. - Laths

There are two laths in the garage opposite one another: one 2 meters long and the other 3 meters long. They fall against each other and lean against the opposite walls of the garage both laths and touch at a height of 70 cm above the garage floor. How wide

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Pythagorean theorem is the base for the right triangle calculator.