Question
In the figure given below, a line segment is drawn parallel to one side of the triangle and the lengths of certain line-segment are marked. Find the value of x in the following:
✓
Answer
$\frac{\text{a}}{\text{a}+1}=\frac{\text{b}}{\text{b}+\text{x}}$By cross multiplication on both sides, we get
$\text{a}\times(\text{b}+\text{x})=\text{b}\times(\text{a}+1)$
$\text{ab}+\text{ax}=\text{ab}+\text{b}$
$\text{ax}=\text{ab}+\text{b}-\text{ab}$
$\text{ax}=\text{ab}+\text{b}-\text{ab}$
$\text{ax}=\text{b}$
$\text{x}=\frac{\text{b}}{\text{a}}$
Hence the value of x is $\frac{\text{b}}{\text{a}}.$
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