SSC CHSL 2024 PYQ — Question 53

The correct answer is option 3 i.e. 3.2.

To find the length of  XY in triangle ABC, we can use the properties of similar triangles. SinceXY is parallel to BC , triangles AXY and  ABC are similar.

Using the properties of similar triangles, we can set up a proportion based on the corresponding sides:

$\frac{AX}{AB} = \frac{XY}{BC}$
We know:
 AB = 5.4 
 BC = 7.2  cm
BX = 3 cm

First, we need to find  AX :
AX = AB - BX = 5.4  cm - 3  cm = 2.4  cm

Now, we can set up the proportion:

$\frac{AX}{AB} = \frac{XY}{BC}$

Substituting the known values:

$\frac{2.4}{5.4} = \frac{XY}{7.2}$

To solve for  XY, we can cross-multiply:

2.4 $\times$ 7.2 = 5.4 $\times$ XY
 

Calculating  2.4 $\times$ 7.2:

2.4 $\times$ 7.2 = 17.28
 

So, we have:

17.28 = 5.4 $\times$ XY
 

Now, divide both sides by 5.4:

XY =$\frac{17.28}{5.4}$ = 3.2 cm

Thus, the length of XY is boxed 3.2 cm.