# Pythagorean theorem + quadratic equation - math problems

#### Number of problems found: 85

• One leg
One leg of a right triangle is 1 foot longer than the other leg. The hypotenuse is 5 feet. Find the lengths of the three sides of the triangle.
• Woman's day
We can easily make a heart for mothers for Woman's day by drawing two semicircles to the two upper sides of the square standing on their top. What is the radius of the circle circumscribed by this heart when the length of the side of the square is 1?
• The sides
The sides of a right triangle form an arithmetic sequence. The hypotenuse is 24 cm long. Determine the remaining sides of the triangle.
• Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?
• Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
• Difference of legs
In a right triangle, the length of the hypotenuse is 65 m, and the difference of legs is 23 m. Calculate the perimeter of this triangle.
• An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
• A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
• 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?
• 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.
• Ratio of sides
Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
• RT sides
Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
• Rectangle
There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of a rectangle.
• Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
• Diagonals of a rhombus 2
One diagonal of a rhombus is greater than the other by 4 cm. If the area of the rhombus is 96 cm2, find the side of the rhombus.
• AP RT triangle
The length of the sides of a right triangle forms an arithmetic progression, and the longer leg is 24 cm long. What are the perimeter and area?
• Isosceles triangle
The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
• Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.