Mathematics: Diagonal ac divides the trapezoid abcd (with bases ad and bc , ad bc) into two similar triangles, △abc and △dca. find ac if bc=4 cm and ad=9 cm.

Diagonal ac divides the trapezoid abcd (with bases

athenadailey8717

10.03.2022

AC= 6 cm

Step-by-step explanation:

It is given that ABCD is a trapezoid

Also AC divides the trapezoid into two similar triangles

ΔABC≈ΔDCA

The ratio of corresponding sides of similar triangles are equal, so we have

$\frac{AB}{CD} =\frac{BC}{AC} =\frac{AC}{AD}$

now we can take

$\frac{BC}{AC} =\frac{AC}{AD}$

$\frac{4}{AC} =\frac{AC}{9}$ ( since BC=4 and AD= 9)

now we cross multiply

$4(9)=AC^{2}$

$AC^{2}=36$

$AC=\sqrt{36}$ (taking square root )

AC= 6 cm

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bigchungus86

18.02.2021

esdtrfguyhijok

Step-by-step explanation:

15/16

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