# Expression of a variable from the formula - high school - math problems

- The perimeter of the rectangle

The length, l, of a rectangle is 4 inches greater than its width, w. The perimeter of the rectangle is at least 30 inches. What inequality shows the range of possible widths of the rectangle? - 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. - Isosceles triangle 10

In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles. - Two-digit number

Digit sum of thinking two-digit natural number is 11. When it exchanging a sequence of digits, given a number which is 27 less than the thinking number. Find out which number I think. - Reciprocal value

How do I calculate a number x that is 9 greater than its reciprocal (1/x)? - Circular railway

The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C? - Square side

If we enlarge the square side a = 5m, its area will increase by 10,25%. How many percent will the side of the square increase? How many percent will it increase the circumference of the square? - Cylinder and its circumference

If the height of a cylinder is 4 times its circumference c, what is the volume of the cylinder in terms of its circumference, c? - Secret treasure

Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure. - Equation 23

Find value of unknown x in equation: x+3/x+1=5 (problem finding x) - 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? - Together m+w

Women 30%. Men are 360 more. How many are together? - Bdf tablet

Detective Harry Thomson has come across a surprising mystery. As part of the weekend's action, the tablet he looked for dropped by 30%. He also recommended this bargain to his friend. However, it came to the shop on Monday, and the tablet was 30% more expe - Rectangle field

The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m? - A rectangle 2

A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths. - Frustum of a cone

A reservoir contains 28.54 m^{3}of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone. - Three altitudes

A triangle with altitudes 4; 5 and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle. - Rectangular garden 2

A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m^{2}. Calculate the size of the garden. - 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=1.2, y=1.7, z=1.45 - Voltmeter range

We have a voltmeter which in the original set measures voltage to 10V. Calculate the size of the ballast resistor for this voltmeter, if we want to measure the voltage up to 50V. Voltmeter's internal resistance is 2 kiloohm/Volt.

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