Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Measurements of a room are
7m50cm,6m&
3m75cm. Find the length of the longest rod that can measure all the three dimensions of the room.

Measurements of a room are $7\mathrm{~m} 50 \mathrm{~cm}, 6 \mathrm{~m} \&$ $3 \mathrm{~m} 75 \mathrm{~cm}$ . Find the length of the longest rod that can measure all the three dimensions of the room.

View step-by-step help

View step-by-step help

Area and perimeter: word problems

Full solution

Q. Measurements of a room are

7\mathrm{~m} 50 \mathrm{~cm}, 6 \mathrm{~m} \&

3 \mathrm{~m} 75 \mathrm{~cm}

. Find the length of the longest rod that can measure all the three dimensions of the room.

Convert to centimeters: Convert all measurements to centimeters for uniformity. $\newline$ $7\text{m} 50\text{cm} = 750\text{cm}$ , $6\text{m} = 600\text{cm}$ , $3\text{m} 75\text{cm} = 375\text{cm}$ .
Find GCD for longest rod: Find the greatest common divisor (GCD) of the three measurements to determine the longest rod that can measure all dimensions. $\newline$ GCD of $750$ , $600$ , and $375$ . $\newline$ Using prime factorization: $\newline$ $750 = 2 \times 3 \times 5^3$ $\newline$ $600 = 2^2 \times 3 \times 5^2$ $\newline$ $375 = 3 \times 5^3$ $\newline$ Common factors are $3$ and $5^2$ . $\newline$ GCD = $3 \times 5^2 = 75\,\text{cm}$ .

More problems from Area and perimeter: word problems

Question

A square window has a perimeter of \(136\) inches. How long is each side?

\newline

\_\_\_\_\_

Posted 1 month ago

Question

What is the greatest possible error for a measurement of

2

\newline

\_\_\_

Posted 2 months ago

Question

What is the percent error for a measurement of

5

?

\newline

If needed, round your answer to the nearest hundredth of a percent.

\newline

\newline

Posted 1 month ago

Question

Which measurement is more precise?

\newline

\newline

29.4

\newline

31

Posted 2 months ago

Question

A new dictionary in the shape of a rectangular prism will have a thickness of

3

inches (in). The volume of the dictionary will be

216 \mathrm{in}^{3}

. What must be the area of the front cover, a face perpendicular to the thickness, in square inches?

Posted 4 months ago

Question

Sako's garden is

6

yards long. What is the length of his garden in feet?

Posted 2 months ago

Question

Avery is designing a large rectangular sign. They want the sign to have an area of

2\,\text{m}^2

\frac{4}{5}\,\text{m}

. How tall should the sign be?

Posted 2 months ago

Question

Find the monthly payment for a

30

100000

4\%

Posted 2 months ago

Question

Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of

15 \frac{1}{2} \text{ m}^2

. Gabriel wants it to be

7 \frac{3}{4}

long. How wide does the planter box need to be?

Posted 2 months ago

Question

An electrician plans to install solar panels on a rectangular section of roof with an area of

180\text{m}^2

. This width of this section of roof is

7\frac{1}{5}

Posted 2 months ago