This is a right triangle, which fits the Pythagorean Theorem, a^2 +b^2 = c^2. The variables a, b, and c all are sides of the triangle, while a and b are the two legs and c is the hypothenuse.

In this problem, we see that 6 and x are the legs and 10 is the hypothenuse. We put 6 as "a" and x as "b" (but it doesn't matter which is a and b) and 10 is c. Therefore, we have the equation:

6^2 + x^2 = 10^2

which further simplifies to:

36 + x^2 = 100

x^2 = 64

and so x would equal 8 (or -8, but it is impossible to have a side length of -8).

Therefore, the missing side is 8.

7 0

3 years ago

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The volume of the rectangular prism is 648 feet. The rectangular base is 6 feet by 9 feet. What is the height of the prism?

IrinaK [193]

Answer:

$h=12ft$

Step-by-step explanation:

The formula one would use for finding the volume of a rectangular prism is as follows:

Volume = length × width × height , $V=l*w*h$

With this in mind, let's plug in the given variables in the question for this formula.

$V=648ft^3$

$l=6ft$

$w=9ft$

$h=$ ?

We don't know the height, but that's just fine. We will plug in all our values and isolate $h$ .

$V=lwh\\648ft^3=(6ft)(9ft)h$

I'm leaving in units just because I want to show that units aren't just for show. They can be used when in doubt of how to go about your math.

$648ft^3=(6ft)(9ft)h\\648ft^3=(54ft^2)h\\\frac{648ft^3}{54ft^2}=\frac{(54ft^2)h}{54ft^2}$

Notice, that the units on the left side cancel out, leaving only the unit $ft$ left next to the solution. In the same way, the units on the right side cancel out too, leaving only $h$ , height.

$\frac{648ft^3}{54ft^2}=\frac{(54ft^2)h}{54ft^2}\\12ft=h$

If involving units only confuses you, like it does for me, you can remove them like so, you just need to know what units your solution uses instead of being able to come to the proper units by using math.

$V=lwh\\648=(6)(9)h\\648=54h\\\frac{648}{54}=\frac{54h}{54}\\12ft=h$

5 0

3 years ago