# Plumber

Plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares so that no waste. Calculate the length of the sides of a square. How many squares cut it?

Result

x =  20 cm
n =  57

#### Solution:

$a = 380 \ cm \ \\ b = 60 \ cm \ \\ \ \\ 380 = 2^2 \cdot 5 \cdot 19 \\ 60 = 2^2 \cdot 3 \cdot 5 \\ \text{GCD}(380, 60) = 2^2 \cdot 5 = 20\\ \ \\ \ \\ x = GCD(a,b) = GCD(380,60) = 20 = 20 \ \text { cm }$
$S_{ 1 } = a \cdot \ b = 380 \cdot \ 60 = 22800 \ cm^2 \ \\ S_{ 2 } = x^2 = 20^2 = 400 \ cm^2 \ \\ \ \\ n = \dfrac{ S_{ 1 } }{ S_{ 2 } } = \dfrac{ 22800 }{ 400 } = 57$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

#### Following knowledge from mathematics are needed to solve this word math problem:

Do you want to calculate least common multiple two or more numbers? Do you want to calculate greatest common divisor two or more numbers?

## Next similar math problems:

1. Present
Gift box has rectangular shape with dimensions of 8×8×3 cm. Miloslav wants to cover with square paper with sides of 18 cm. How much paper left him?
2. Windows
Calculate the area of masonry to build wall with dimensions of 9 m × 4 m with 4 windows of size 64 cm × 64 cm.
3. Square grid
Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm2 and circumference 12 cm and that their sides is in square grid.
4. Glass
At the glass shop we have to cut 8 sheets of glass. Each was shaped a square with sides of 18 cm. We paid 44 CZK. How much is a 1 m2 of glass?
5. Garden
How many steps of 76 cm circumvent square garden with area 1.8 ha?
6. Gardens
The garden has the square shape with circumference 124 m. Divide it into two rectangular gardens, one should circumference 10 meters more than the second. What size will have a gardens?
7. Tiles
Hall has dimensions 325 &time; 170 dm. What is the largest size of square tiles that can be entire hall tiled and how many we need them?
8. 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.
9. Mr. Zucchini
Mr. Zucchini had a rectangular garden whose perimeter is 28 meters. Content area of the garden 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
10. Two squares
Two squares whose sides are in the ratio 5:2 have sum of its perimeters 73 cm. Calculate the sum of area this two squares.
11. Rectangles
Calculate how many squares/rectangles of size 4×3 cm can be cut from a sheet of paper of 36 cm × 32 cm?
12. Maximum area of rhombus
Calculate the interior angles at which equilateral rhombus has a maximum area.
13. Prism
Three cubes are glued into prism, sum of the lengths of all its edges is 115 cm. What is the length of one edge of the original cube?
14. Coins
Harvey had saved up a number of 2-euro coins. He stored coins in a single layer in a square. Left 6 coins. When he make square, which has one more row, missing 35 coins. How many euros he have?
15. Hexagon - MO
The picture shows the ABCD square, the EFGD square and the HIJD rectangle. Points J and G lie on the side CD and is true |DJ|