Question
In the adjoining figure, find AC.
✓
Answer
Given: In the figure we are given AD = 6cm, BD = 9cm, AE = 8cm
To Find: AC
According to Basic Proportionality Theorem, if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
In $\triangle\text{ABC}, \text{DE}||\text{BC}$
So,
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\frac{6}{9}=\frac{8}{\text{EC}}$
$\text{EC}=\frac{8\times9}{6}$
EC = 12cm
Now,
AC = AE + EC
AC = 8 + 12
AC = 20cm.
To Find: AC
According to Basic Proportionality Theorem, if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
In $\triangle\text{ABC}, \text{DE}||\text{BC}$
So,
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\frac{6}{9}=\frac{8}{\text{EC}}$
$\text{EC}=\frac{8\times9}{6}$
EC = 12cm
Now,
AC = AE + EC
AC = 8 + 12
AC = 20cm.
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