In trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).
What is trapezoid?
" 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,
[tex]\frac{AE}{EC}=\frac{AB}{CD}[/tex]
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,
[tex]\frac{5.2}{6.5}=\frac{AB}{10.5}[/tex]
⇒ [tex]AB = \frac{(10.5)(5.2)}{6.5}[/tex]
⇒[tex]AB = 8.4[/tex] units
Hence, in trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).
Learn more about trapezoid here
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