One of the basic question from similarity chapter in which we have been asked to find the length of sides of triangle from the given figure
ML Aggarwal Avichal Publication, Similarity, Chapter 13, question no 8(i)
Rajan@2021Guru
In the figure given below, AB∥DE,AC=3 cm,CE=7.5 cm and BD=14 cm. Calculate CB and DC.
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From the question it is given that,
AB∥DE
AC=3cm
CE=7.5cm
BD=14cm
From the figure,
∠ACB=∠DCE [because vertically opposite angles]
∠BAC=∠CED [alternate angles]
Then, △ABC∼△CDE
So, AC/CE=BC/CD
3/7.5=BC/CD
By cross multiplication we get,
7.5BC=3CD
Let us assume BC=x and CD=14−x
7.5×x=3×(14−x)
7.5x=42−3x
7.5x+3x=42
10.5x=42
x=42/10.5
x=4
Therefore, BC=x=4cm
CD=14−x
=14−4
=10cm.