Math homework help????? please?
heres what it says on the paper. Using proportions, you can calculate the dimensions of objects without having to measure them. solve the problems that follow...
heres the problem
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amy is 5 feet tall and casts a 4-foot shadow. the pine tree has an 8 foot shadow. how tall is the pine tree..????
Please help me understand how to do this
Here's the proportion:
Height is to shadow as height is to shadow. Let x represent the unknown -- the height of the tree.
5/4 = x/8
Cross multiply:
4x = 40
Solve for x.
x = 40/4
x = 10
The tree is 10 feet tall.
To solve this problem using proportions, we can set up a ratio between the height of Amy and the length of her shadow. Then, we can use this ratio to find the height of the pine tree.
First, let's write down the ratio for Amy:
Height of Amy / Length of Amy's shadow = 5 feet / 4 feet
Now, we can set up the equation using the ratio:
Height of Pine Tree / Length of Pine Tree's shadow = 5 feet / 4 feet
We know that the length of the pine tree's shadow is 8 feet. So, we can substitute it into the equation:
Height of Pine Tree / 8 feet = 5 feet / 4 feet
To solve for the height of the pine tree, we can cross-multiply and then solve for the unknown variable. Cross-multiplying means multiplying the numerator of one fraction by the denominator of the other fraction. It can be written as follows:
(Height of Pine Tree) * (4 feet) = (8 feet) * (5 feet)
Now, let's simplify the equation:
4 feet * Height of Pine Tree = 8 feet * 5 feet
Cancel out the feet on the left side and simplify the right side:
4 * Height of Pine Tree = 40 feet
Finally, divide both sides of the equation by 4 to isolate the height of the pine tree:
Height of Pine Tree = 40 feet / 4
Therefore, the height of the pine tree is 10 feet.
In summary, by setting up and solving a proportion involving the height of Amy and the length of her shadow, we can find the height of the pine tree without directly measuring it.