Looking at a trapezoid like this:
http://content.answers.com/main/content/wp/en/b/b7/Isosceles_trapezoid.jpg
top - 10 ft
bottom - 16 ft
left side - 5 ft
right side - 5 ft
The question:
What is the distance between the top and bottom?
A. 3
B. 4
C. 5
D. 10
E. 16
Please explain your answer.
2007-07-20 11:07:03 · 8 answers · asked by sameperson247 2 in Science & Mathematics ➔ Mathematics
Taken from a 06-07 ACT practice test.
2007-07-20 11:09:00 · update #1
I drew a diagram to work this out; it's at http://i72.photobucket.com/albums/i168/hyio/trapezoid_question.jpg
2007-07-20 11:30:53 · answer #1 · answered by grobanite_hyio 2 · 0⤊ 0⤋
Drop a perpendicular from the top left corner ot the trapezoid to the base. This will form a right triangle with hypotenuse =5. The short leg = (16-10)/2 = 3. This works only because the trapezoid is isosceles.
So the altitude (the distance between top and bottom) is sqrt(5^2-3^2) = 4
2007-07-20 11:23:21 · answer #2 · answered by ironduke8159 7 · 1⤊ 0⤋
Make a sketch.
Your trapezoid is symmetrical because right and left sides are equal.
Imagine two right triangles at each side with the hypotenuse being 5 and the base 3 (because the difference between the upper and lower sides is 6).
Then the square of the hypotenuse is 25 and the square of the base is 9, then the height square must be 16 and its square root 4.
The answer is 4 ft.
.
2007-07-20 11:33:28 · answer #3 · answered by NaughtyBoy 3 · 0⤊ 0⤋
5
2007-07-20 11:14:02 · answer #4 · answered by Anonymous · 0⤊ 1⤋
Drop 2 perpendiculars so that you form 2 right triangles and a rectangle. The rectangle has length of 10'. Since the bottom is 16' the 2 bases of the right triangles are 8' or one of the bases is 4'. By doing this you form 2 right triangles of hypotenuse 5 and base is 4, but this a 3-4-5 right triangle--thus the altitude is 3 or answer A
2007-07-20 11:16:10 · answer #5 · answered by dr_no4458 4 · 0⤊ 1⤋
B-4
The top is 6 shorter than the bottom, and the trap. is an isosceles trap, so the difference is split 3 per side.
The hight, the leg, and part of the base make a 3-4-5 right triangle, so the hight has to be 4.
2007-07-20 11:19:43 · answer #6 · answered by Felix S 2 · 1⤊ 0⤋
the difference between the top and bottom is 6, 16-10
if you drop a vertical from the leftmost vertex of the trapezoid, you create a right triangle.
the base of this triangle would be 3 (one half of 6) and the hypotenuse is 5
pythagorean theorem states a^2+b^2=c^2
a is 3 and c is 5
9+b^2=25
b^2=25-9=16
square root of 16 is four, so the answer is 4
2007-07-20 11:12:22 · answer #7 · answered by Kris Z 4 · 2⤊ 0⤋
the answer is 4
(excuse my english)
1st, subtract 10 from 16, 16-10 = 6
2nd, divide it by 2, 6/2=3, to get the length below the side length.
the do trigonometry, x= height = sqroot(5^2 - 3^2) = 4
2007-07-20 11:16:56 · answer #8 · answered by Anonymous · 1⤊ 0⤋