# Square + prime numbers - practice problems

#### Number of problems found: 26

- The land

The land, which has dimensions of 220 m and 308 m, the owner wants to divide into equally large square plots with the largest possible area. How long will one side of the plot be? - Square gardens

The gardening colony with dimensions of 180 m and 300 m is to be completely divided into equally large square areas with the largest possible area. Calculate how many such square areas can be obtained and determine the side length of the square. - How many

How many different rectangles with integer page lengths have an area S = 60 cm²? - Largest squares

How many of the largest square sheets did the plumber cut the honeycomb from 16 dm and 96 dm? - Rectangles

How many different rectangles can be made from 60 square tiles of 1 m square? Find the dimensions of these rectangles. - The tickets

The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices. - Two gears

A large gear will be used to turn a smaller gear. The large gear will make 75 revolutions per minute. The smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM. ] - Cutting paper

Divide a rectangular paper with dimensions 220mm and 308mm into squares of the same size so that they are as large as possible. Specify the length of the side of the square. - Two rectangles

I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm². What dimensions can this large rectangle have? Write all options. Explain your calc - Glass panel

A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut? - Pagans

Elena cut out same circle-shaped pagans and put them on a rectangular sheet so that the neighboring pagans were touching each other and the pagans were touching the walls of the sheet on the edges. Each pagans occupied 28.26 cm² of the bottom of the sheet - Tiles

How many tiles of 20 cm and 30 cm can build a square if we have a maximum of 100 tiles? - Square tiles

The room has dimensions of 12 meters and 5.6 meters. Determine the number of square tiles and their largest dimension to exactly cover the floor. - Mr. Zucchini

Mr. Zucchini had a rectangular garden whose perimeter is 28 meters. The garden's content area filled just four square beds, whose dimensions in meters are expressed in whole numbers. Determine what size could have a garden. Find all the possibilities and - Primes 2

For what primes p,q,r is true: p^{2}-(q+r)^{2}=647 - Paper squares

The paper rectangle measuring 69 cm and 46 cm should be cut into as many squares as possible. Calculate the lengths of squares and their number. - Trams 2

Square passes two lines of tram. One running every nine minutes, a second interval of 15 minutes. Exactly at 12 o'clock arrived two tram lines in the square. How soon should a similar situation arise again? - Tiles

The room has dimensions 12 m and 5.6 m. Determine the number of square tiles and their largest possible size to cover them room's floor. - Plumber

The plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it? - Square room

What is the size of the smallest square room, which can pave with tiles with dimensions 55 cm and 45 cm? How many such tiles is needed?

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Square practice problems. Prime numbers - practice problems.