Im the figure given below, AB || DE, AC = 3cm , CE = 7.5cm and BD = 14cm. 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.
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