# Quadratic equation + triangle - math problems

#### Number of problems found: 82

- Integer sides

A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side? - 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 - Sphere equation

Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - 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. - RT perimeter

The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference. - 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? - 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. - Right angled triangle

Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of 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? - 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. - RT sides

Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm. - Perimeter of RT

Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm^{2}. - 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. - Euclid theorems

Calculate the sides of a right triangle if leg a = 6 cm, and a section of the hypotenuse, which is located adjacent to the second leg b is 5cm. - Euclid1

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

The height of the pole before the storm is 10 m. After a storm when they come to check it they see that on the ground from the pole blows part of the column. Distance from the pole is 3 meters. At how high was the pole broken? (In fact, a rectangular tria - 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. - Right triangle from axes

A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment? - Prove

Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - Isosceles triangle 9

Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm, and the altitude is 24cm. Find the area of the isosceles triangle.

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