Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The shadow of a meter stick measures 1.2 m1.2\,\text{m} long. At the same time, a nearby tree casts a shadow that is 21.4 m21.4\,\text{m} long. How tall is the tree?

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 7right chevron icon
Add, subtract, multiply, and divide decimals: word problemsright chevron icon

Full solution

Q. The shadow of a meter stick measures 1.2 m1.2\,\text{m} long. At the same time, a nearby tree casts a shadow that is 21.4 m21.4\,\text{m} long. How tall is the tree?
  1. Identify similar triangles: Identify the similar triangles.\newlineThe meter stick and its shadow form a right-angled triangle, as does the tree and its shadow. Since the sun's rays are parallel, the triangles are similar, which means the ratios of their corresponding sides are equal.
  2. Set up proportion: Set up the proportion using the corresponding sides of the similar triangles.\newlineLet the height of the tree be h h meters. The ratio of the height of the meter stick to its shadow is equal to the ratio of the height of the tree to its shadow.\newlineSo, we have 11.2=h21.4 \frac{1}{1.2} = \frac{h}{21.4} .
  3. Solve for height: Solve the proportion for h h to find the height of the tree.\newlineCross-multiply to solve for h h :\newline1×21.4=1.2×h 1 \times 21.4 = 1.2 \times h \newline21.4=1.2h 21.4 = 1.2h
  4. Divide to isolate height: Divide both sides of the equation by 11.22 to isolate h h .\newline21.41.2=h \frac{21.4}{1.2} = h \newlineh≈17.8333 h \approx 17.8333 meters

More problems from Add, subtract, multiply, and divide decimals: word problems

Question
Convert the following repeating decimal to a fraction in simplest form.\newline.68‾ .6 \overline{8} \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
Convert the following repeating decimal to a fraction in simplest form.\newline.94‾ .9 \overline{4} \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
Convert the following repeating decimal to a fraction in simplest form.\newline.96‾ .9 \overline{6} \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
Which expression is equivalent to 99.7−(−57.9) 99.7-(-57.9) ?\newline99.7−57.9 99.7-57.9 \newline57.9−99.7 57.9-99.7 \newline−57.9−99.7 -57.9-99.7 \newline99.7+57.9 99.7+57.9
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the value of x x in the equation below.\newlinex−13.6=7.6 x-13.6=7.6 \newlineAnswer: x= x=
Get tutor helpright-arrow

Posted 2 months ago

Question
A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she dropped 6868.11 feet. How many feet had she been below sea level, if she was 155155.44 feet below sea level after she dropped?\newlineAnswer: □\square feet
Get tutor helpright-arrow

Posted 2 months ago

Question
A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she went down 3636.33 feet. How many feet had she been below sea level, if she was 9999.77 feet below sea level after she went down?\newlineAnswer: □\square feet
Get tutor helpright-arrow

Posted 2 months ago

Question
A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she descended 2222 feet. How many feet had she been below sea level, if she was 5252.33 feet below sea level after she descended?\newlineAnswer: □\square feet
Get tutor helpright-arrow

Posted 2 months ago

Question
A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she dropped 8888.66 feet. How many feet had she been below sea level, if she was 182182.55 feet below sea level after she dropped?\newlineAnswer: □\square feet
Get tutor helpright-arrow

Posted 2 months ago

Question
A scientist was in a submarine, 4141.44 feet below sea level, studying ocean life. Over the next ten minutes, she rose 3333.66 feet. How many feet was she now below sea level?\newlineAnswer: □\square feet
Get tutor helpright-arrow

Posted 2 months ago

View all (48)