In trapezoid ABCD, Line AB is parallel to CD. If AE=5.2, AC=11.7 and CD=10.5, what is the length of AB to the nearest tenth?
2 answers:
In trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).
<h3>What is trapezoid?</h3>
" Trapezoid is defined as the quadrilateral whose one pair of opposite side is parallel."
According to the question,
Given
Length of AE=5.2
Length of AC=11.7
Length of CD=10.5
As shown in figure
In trapezoid ABCD,
AB is parallel to CD, AC is the transversal.
AC and BD intersect at point E.
In ΔABE and ΔCDE,
∠BAE ≅∠ECD
∠ABE ≅∠EDC
By AA theorem,
ΔABE ~ ΔCDE
Therefore,
AE + EC = AC
⇒ 5.2 + EC = 11.7
⇒ EC = 11.7 - 5.2
⇒ EC = 6.5units
Substitute the value in the given proportion we get,
⇒
⇒ units
Hence, in trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).
Learn more about trapezoid here
#SPJ2
You might be interested in
9514 1404 393
Answer:
- y -9 = 2(x -1) . . . point-slope form
- y = 2x +7 . . . . slope-intercept form
- 2x -y = -7 . . . . standard form
Step-by-step explanation:
Perhaps you want the equation of the line that goes through these two points.
The slope of the line can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (9 -3)/(1 -(-2)) = 6/3 = 2
We can use one of the points to write the equation in point-slope form:
y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)
For slope 2 and point (1, 9) the equation is ...
y -9 = 2(x -1) . . . . equation in point-slope form
__
We can eliminate parentheses and get y by itself to put the equation into slope-intercept form.
y -9 = 2x -2
y = 2x +7 . . . . . . equation in slope-intercept form
__
With a little further rearranging, we can put this into standard form. We can get that by adding -7-y to both sides of the equation.
2x -y = -7 . . . . . equation in standard form
