Question

Given $△ABC$, find the values of $p$ and $q$

• A. 4 cm, 5 cm
• B. 6 cm , 5 cm
• C. 7 cm , 6 cm
• D. 7.2 cm, 6.4 cm

Answer 1

The correct option is D 7.2 cm, 6.4 cm

The $△ABC$ is:


Now a line $XY$ is drawn so that it is parallel to $BC$. And we are also told that it divides $BA$ in the ratio $4:5$ meaning that the top $4$ to the bottom $5$.

So now we have to find length $BC$ and $CY$.


Figure out $5:4$ part breaking down. The total length $AB$ is divided into $2$ pieces. One is $5$ cm other is $4$ cm. When adding up it becomes $9$ cm.

$AX$ has a length of $5$ cm, $XB$ has a length of $4$ cm, $BC$ has a length of $p$ cm, $AY$ has a length of $8$ cm and $YC$ has a length of $q$ cm.

Parallel lines are cut by transversals.
$\therefore △ABC$ is similar to $△AXY$ (similar by angle-angle)

We know that $XY\parallel BC$
That's the case then we can think about these $2$ parallel lines being crossed by $2$ transversals.One is $AB$ and other is $AC.$ And corresponding angles will be congruent.


For transversal $AB:\angle ABC=\angle AXY$
For transversal $AC:\angle ACB=\angle AYX$

$△ABC$ is similar to $AXY$
So we can see those two triangles are similar. So that means that the corresponding parts will always be in same proportion. So the ratio of corresponding parts will correspond to the ratio of other corresponding parts.

So to find the length of $BC$
$\frac{p}{4}=\frac{9}{5}$
$\Rightarrow 5\cdot p=36$
$\Rightarrow p=\frac{36}{5}$
$\Rightarrow p=7.2$ cm

So to find the length of $CY$
$\frac{8+q}{8}=\frac{9}{5}$
$\Rightarrow 5\cdot (8+q)=8\times 9$
$\Rightarrow 40+5q=72$
$\Rightarrow 5q=72-40$
$\Rightarrow 5q=32$
$\Rightarrow q=\frac{32}{5}$ cm
$\Rightarrow q=6.4$ cm