Question

$s$ and $t$ are transversals cutting a set of parallel lines such that a segment of length $3$ in $s$ corresponds to a segment of length $5$ in $t.$ What is the length of segment in $t$ corresponding to a segment of length $12$ in $s?$

• A. $20$
• B. $\frac{36}{5}$
• C. $14$
• D. $\frac{5}{4}$

Answer 1

The correct option is A $20$

Let $L1,L2,L3,L4,L5$ be a set of parallel lines.

$s$ and $t$ are the transversals cutting the parallel lines $L1,L2,L3,L4,L5$ , as shown in the above fig...

Let $s1,s2,s3,s4$ be the line segments on transversal $s$ and $t1,t2,t3,t4$ be the line segments on transversal $t$, formed cutting the parallel lines $L1,L2,L3,L4,L5$

Given that, a segment of length $3$in $s$ corresponds to a segment of length $5$ in $t$.

Say, $s1=3,t1=5$

To find: the length of segment in $t$ corresponding to a segment of length $12$ in $s$.

Say, $s2=12,t2=?$

The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and it intersects the other two sides, then it divides those sides proportionally.

On extending the tranversals $s$ and $t$, they join at $A$. join the other two ends with line $BC$ , forming a triangle $-△ABC$

$\therefore \frac{s1}{s2}=\frac{t1}{t2}$

$\frac{3}{12}=\frac{5}{t2}$

$t2=\frac{12\times 5}{3}$

$t2=20$

$\therefore$ The length of segment in $t$ corresponding to a segment of length $12$ in $s$ is $20$