Two sides of a triangle are 10 cm and 15 cm and the base is 20 cm long . If another triangle similar to the first triangle has the base measuring 32 cm , then other two sides of the triangle are

Options

A. 16 cm , 24 cm
B. 12 cm , 28 cm
C. 15 cm , 25 cm
D. 18 cm , 22 cm

Answer

To solve the question step by step, we will use the properties of similar triangles.

### Given:
- Triangle ABC with sides AB = 10 cm, BC = 15 cm, and base AC = 20 cm.
- A similar triangle DEF with base DE = 32 cm.

### Step 1: Set up the proportion for similar triangles
Since triangle ABC is similar to triangle DEF, we can set up the following proportion based on the corresponding sides:
\[ \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} \]

### Step 2: Substitute known values into the proportion
We know:
- AB = 10 cm
- AC = 20 cm
- DE = 32 cm
- BC = 15 cm

We need to find EF and DF. We can start with the first part of the proportion:
\[ \frac{10}{DE} = \frac{20}{32} \]

### Step 3: Solve for DE
Cross-multiply to solve for DE:
\[ 10 \times 32 = 20 \times DE \]
\[ 320 = 20 \times DE \]
Now, divide both sides by 20:
\[ DE = \frac{320}{20} = 16 \text{ cm} \]

### Step 4: Use the second part of the proportion to find EF
Now we can use the second part of the proportion:
\[ \frac{15}{DF} = \frac{20}{32} \]

### Step 5: Solve for DF
Cross-multiply to solve for DF:
\[ 15 \times 32 = 20 \times DF \]
\[ 480 = 20 \times DF \]
Now, divide both sides by 20:
\[ DF = \frac{480}{20} = 24 \text{ cm} \]

### Conclusion
The lengths of the other two sides of triangle DEF are:
- DE = 16 cm
- DF = 24 cm