The trapezoid diagonal is 6, it divides the trapezoid into two similar triangles. Find the length of the lower base of the trapezoid if the bigger base is 12?

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The trapezoid diagonal is 6, it divides the trapezoid into two similar triangles. Find the length of the lower base of the trapezoid if the bigger base is 12?

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Answer 1 · 2017-10-09T06:04:27

$3$ $3$ units

Explanation:

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As shown in the figures, $A D and B C$ $AD and BC$ are the bases of the trapezoid $A B C D$ $ABCD$ ,
As $A D$ $AD$ is parallel to $B C$ $BC$ ,
$\Rightarrow ∠ B C D = ∠ C A D = x$ $=> angleBCD=angleCAD=x$
Given that the diagonal $A C$ $AC$ divides the trapezoid into two similar triangles, namely, $DeltaABC, and DeltaDCA$ , and as $angleADC != angleABC$
$=> angleCAB=angleADC=y$
$=> (BC)/(AC)=(CA)/(DA)$
$=> (BC)/6 = 6/(12)$
$=> BC=3$

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The trapezoid diagonal is 6, it divides the trapezoid into two similar triangles. Find the length of the lower base of the trapezoid if the bigger base is 12?

1 Answer

Explanation:

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