In a right angled triangle if hypotenuse is 20 cm and ratio of other two sides is 4 : 3, the lengths of the other two sides are

Options

A. 4 cm, and 3 cm
B. 8 cm, and 6 cm.
C. 12 cm, and 9 cm.
D. 16 cm, and 12 cm.

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the problem
We have a right-angled triangle with a hypotenuse of 20 cm and the lengths of the other two sides in the ratio of 4:3. We need to find the lengths of these two sides.

### Step 2: Assign variables based on the ratio
Let the lengths of the two sides be \(4x\) and \(3x\), where \(x\) is a common multiplier.

### Step 3: Apply the Pythagorean theorem
According to the Pythagorean theorem, in a right-angled triangle:
\[ \text{(side1)}^2 + \text{(side2)}^2 = \text{(hypotenuse)}^2 \]
Substituting the values we have:
\[ (4x)^2 + (3x)^2 = (20)^2 \]

### Step 4: Simplify the equation
Calculating the squares:
\[ 16x^2 + 9x^2 = 400 \]
Combine like terms:
\[ 25x^2 = 400 \]

### Step 5: Solve for \(x^2\)
Divide both sides by 25:
\[ x^2 = \frac{400}{25} \]
\[ x^2 = 16 \]

### Step 6: Solve for \(x\)
Taking the square root of both sides:
\[ x = \sqrt{16} = 4 \]

### Step 7: Find the lengths of the sides
Now substitute \(x\) back into the expressions for the sides:
- First side: \(4x = 4 \times 4 = 16 \text{ cm}\)
- Second side: \(3x = 3 \times 4 = 12 \text{ cm}\)

### Final Answer
The lengths of the other two sides are 16 cm and 12 cm.

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