A right prism has bases that are isosceles trapezoids which have sides of length 16, 25, 25, and 30. The volume of the prism is 5520. What is the Height?

The height is equal to 10.

Step-by-step explanation:

With an isosceles trapezoid, the two legs are the same, and then the two bases. There are 2 sides given that are the same: 25. So now we know that the two legs are 25, and the two bases are 16 and 30 (doesn't really matter which length goes with which base).

To find the volume of an isosceles trapezoid, you need to use the formula   · · .

So, to find , which is the trapezoid height, we need to use the Pythagorean Theorem. We know that the bottom base is 30, so when we draw altitudes from the top base to the bottom base, they are the heights of the trapezoid. The two triangles formed from the altitudes are congruent (I could prove it but just trust me that they are). The rectangle that formed has the top and bottom sides equalling 16. So now we know that the triangles that were formed have bases of 7 because of Part-Whole Postulate (PWP). Since the sides are given as 25, we can find the missing side, which happens to be the height of the triangle, using the Pythagorean Theorem.

The equation would be:  . If you do that math, you get after simplifying. Now you bring the 49 to the other side and subtract, leaving you with . Now you have to square root both sides, and you should end up with h=24.  

Now that we know the height, we can substitute it:   · · =5520 turns into

17 1/3

step-by-step explanation:

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3