Question

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?

Answer 1

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Answer 2

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,

$\frac{AE}{EC}=\frac{AB}{CD}$

  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,

   $\frac{5.2}{6.5}=\frac{AB}{10.5}$

⇒ $AB = \frac{(10.5)(5.2)}{6.5}$

⇒$AB = 8.4$ units

Hence, in trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).

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