In a `DeltaABC` , XY is drawn parallel to BC, cutting sides at X and Y, where AB = 4.8 cm, BC = 7.2 cm and BX = 2 cm. What is the length of XY ?

Options

A. 4 cm
B. 4.1 cm
C. 4.2 cm
D. 4.3 cm

Answer

To find the length of XY in triangle ABC where XY is drawn parallel to BC, we can use the properties of similar triangles. Here’s a step-by-step solution:

### Step 1: Understand the given information
We have a triangle ABC with:
- AB = 4.8 cm
- BC = 7.2 cm
- BX = 2 cm

### Step 2: Calculate AX
Since X is a point on AB, we can find AX using the formula:
\[ AX = AB - BX \]
Substituting the known values:
\[ AX = 4.8 \, \text{cm} - 2 \, \text{cm} = 2.8 \, \text{cm} \]

### Step 3: Establish similarity of triangles
Since XY is parallel to BC, triangles AXY and ABC are similar by the Basic Proportionality Theorem (or Thales' theorem). This means that the ratios of corresponding sides are equal.

### Step 4: Set up the ratio of corresponding sides
From the similarity of triangles AXY and ABC, we can write:
\[ \frac{XY}{BC} = \frac{AX}{AB} \]
Substituting the known values:
\[ \frac{XY}{7.2} = \frac{2.8}{4.8} \]

### Step 5: Cross-multiply to solve for XY
Cross-multiplying gives us:
\[ XY \cdot 4.8 = 2.8 \cdot 7.2 \]
Calculating the right side:
\[ 2.8 \cdot 7.2 = 20.16 \]
Now we have:
\[ XY \cdot 4.8 = 20.16 \]

### Step 6: Solve for XY
To find XY, divide both sides by 4.8:
\[ XY = \frac{20.16}{4.8} \]
Calculating this gives:
\[ XY = 4.2 \, \text{cm} \]

### Conclusion
The length of XY is 4.2 cm.

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