If the base of a trapeziod is 8x+4, the midsegment is 5x+4, and the top is 3x+2, then find the length of the midsegment. Can someone please help me? if you can, explain how to do it.
2006-12-01 03:46:26 · 5 answers · asked by dani 1 in Science & Mathematics ➔ Mathematics
The difference between the base and midsegment is the same as the difference between the midsegment and the top. So:
8x+4 - (5x+4) = 5x+4 - (3x+2)
8x + 4 - 5x -4 = 5x + 4 - 3x -2
3x = 2x+2
x=2
so midsegment = 5(2) + 4 = 14
2006-12-01 03:51:29 · answer #1 · answered by Jim R 3 · 0⤊ 0⤋
The length of the midsegment (also called the median) of a trapezoid is (AB + CD) / 2 ---- where AB is the length of the top segment and CD is the length of the base segment.
For this problem, then, using the above formula for the length of the midsegment we find that the length is (3x+2 + 8x+4) / 2, which simplifies to (11x+6) / 2
Since we are given that the midsegment is also equal to 5x + 4, we can write:
(11x + 6) / 2 = 5x + 4 <--- this is the critical step; it forms an equation we can solve.
To solve the equation, we'll multiply both sides by 2:
11x + 6 = 10x + 8
subtract 6 from both sides
11x = 10x + 2
subtract 10x from both sides
x = 2
...and we have our answer.
2006-12-01 04:05:03 · answer #2 · answered by Mark H 4 · 0⤊ 0⤋
The length of the midsegment of a trapezoid is equal to half the sum of the lengths of the bases. So you just need to write 5x + 4 = (1/2)*(8x + 4 + 3x + 2) and solve it algebraically.
2006-12-01 03:49:45 · answer #3 · answered by DavidK93 7 · 0⤊ 0⤋
I believe the midsegment is the average of the top and bottom, so
(8x+4 + 3x+2)/2 = 5x+4.
Solve for x, plug it into 5x+4, and voilà !
2006-12-01 03:50:23 · answer #4 · answered by Anonymous · 0⤊ 0⤋
How about you do your own homework?
2006-12-01 03:49:36 · answer #5 · answered by Anonymous · 0⤊ 2⤋