Expression of a variable from the formula + Pythagorean theorem - practice problems
Number of problems found: 601
- The rhombus (a,d)
Find the area of a rhombus, one side of which measures 20 cm, and one diagonal 24 cm.
- A field
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m and the non parallel sides are 14 m and 13 m. Find the area of the field.
- Triangle 90
Triangle made by 6 cm 4.5 cm and 7.5 cm. what angles does it make?
- Three inscribed objects
A circle is inscribed in a square. An equilateral triangle of side 4√3 is inscribed in that circle. Find the length of the diagonal of the square.
- Two circles 3
Two circles are inscribed in a square whose side is 4 cm. Find the radius of the smaller circle.
- South and then east
William walks 16 m south from his house and turns east to walk 63 m to reach his friend's house. While returning, he walks diagonally from his friend's house to reach back to his house. What distance did he walk while returning?
- PQR - Euclid
Find the length of line segment PR - leg of the right triangle PQR. PQ=17 cm PS=15 cm QS=8 cm; Point S is the height touch point with a hypotenuse of the RQ.
- A tree 2
A tree is broken at a height of 6 m from the ground and its top touches the ground at a distance of 8 m from the base of the tree. Find the original height of the tree.
- Circle inscribed square
What is the area of the circle that can be inscribed in a square of 10 cm?
- Rhombus 36
Rhombus ABCD with side 8 cm long has diagonal BD 11.3 cm long. Find angle DAB.
- Cuboid - sum of edges length
Calculate the cuboid's dimensions if the sum of its edges is 19 cm. The body's diagonal size is 13 cm, and its volume is 144 cm³. The total surface area is 192 cm².
- FGH right triangle
Given a right triangle with leg lengths f and g, and hypotenuse h, if f = 7 cm and h = 11.2 cm, what is g?
- A right triangle
A right triangle has legs with lengths of 24 cm and 21 cm if the length of the hypotenuse, in cm, can be written in the form of 3 sqrt(d), then what is the value of d?
- General right triangle
In a right triangle, if a =x+34 and b = x and c= 50, then solve for x. Side c is a hypotenuse. Then discuss the case when a or b is a hypotenuse.
- Compound fractions
Solve the compound fraction, use the known formulas, and shorten the: (4a²-12a+9)/(4a-6)
- Circumference 83645
The area of a right triangle is 240 cm². Determine its circumference if the given lengths are suspended in a ratio of 5:12.
- Quadrilateral pyramid
The volume of a regular quadrilateral pyramid is 72 cm³. Its height is equal to the length of the base edge. Calculate the length of the base and the surface of the pyramid.
- Quadrilateral 83254
What is the volume of a regular quadrilateral pyramid if its base edge a = √18 cm and side edge b = 5 cm?
- Hypotenuses 83154
In a right-angled triangle ABC with a right angle at the vertex C, the magnitudes of the hypotenuses are given ta=5, tb=2√10. Calculate the side sizes of triangle ABC and the circle's radius described by this triangle.
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