# Pythagorean theorem + system of equations - math problems

- Block or cuboid

The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block. - Three faces of a cuboid

The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is. - Three parallels

The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle. - 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. - 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=1.3, y=1, z=1.2 - 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. - Touch x-axis

Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. - AP RT triangle

The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area? - Sphere from tree points

Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - Right triangle eq2

Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70. - Solid cuboid

A solid cuboid has a volume of 40 cm^{3}. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - A bridge

A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. - 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? - Isosceles trapezoid

Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high. - Diamond diagonals

Calculate the diamond's diagonal lengths if its content is 156 cm^{2}and the side length is 13 cm. - Nice prism

Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm. - Rectangle

The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides. - Body diagonal

The cuboid has a volume of 32 cm^{3}. Its side surface area is double as one of the square bases. What is the length of the body diagonal? - Trapezoid

trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area? - Triangle - is RT?

Triangle has a circumference of 90 cm. Side b is 1 cm longer than c, side c is 31 cm longer than side a. Calculate the length of sides and determine whether triangle is a right triangle.

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