In triangle ADC length of segment CD = 9.8units .
What are similar triangles?
"Two triangles are said to be similar if the ratio of the their corresponding sides are in proportion or their corresponding angles are of equal measure."
Formula used
For two similar triangles ΔABC and ΔCAD
(AB /AC) =(AC / CD)
According to the question,
As per the diagram,
In ΔABC and ΔADC we have,
Given ,m ∠ABC = m ∠CAD (each 90°)
AB || CD , AC is the transversal.
Therefore,
m ∠BAC = m ∠ACD (Alternate angles between parallel lines)
By AA theorem of similar triangles,
ΔABC ~ ΔCAD
⇒ (AB /AC) = (AC / CD) ( Condition for similar triangles)
Substitute the value as mentioned in diagram we get,
⇒( 5 / 7) = ( 7 / CD)
⇒ CD = ( 7× 7) / 5
⇒ CD = 9.8 units
Hence, Option(D) is the correct answer.
Learn more about similar triangle here
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