Find the ara of a right-angled triangle with hypotenuse 25 cm and altitude 24 cm.

Answer

To find the area of a right-angled triangle with a hypotenuse of 25 cm and an altitude of 24 cm, we can follow these steps:

### Step 1: Understand the triangle
We have a right-angled triangle where:
- Hypotenuse (AC) = 25 cm
- Altitude (AB) = 24 cm

### Step 2: Use the Pythagorean theorem
In a right-angled triangle, the Pythagorean theorem states:
\[ AB^2 + BC^2 = AC^2 \]

Substituting the known values:
\[ 24^2 + BC^2 = 25^2 \]

### Step 3: Calculate the squares
Calculate \( 24^2 \) and \( 25^2 \):
- \( 24^2 = 576 \)
- \( 25^2 = 625 \)

So we have:
\[ 576 + BC^2 = 625 \]

### Step 4: Solve for BC
Now, isolate \( BC^2 \):
\[ BC^2 = 625 - 576 \]
\[ BC^2 = 49 \]

Now, take the square root to find \( BC \):
\[ BC = \sqrt{49} \]
\[ BC = 7 \text{ cm} \]

### Step 5: Calculate the area of the triangle
The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]

Here, we can take:
- Base (BC) = 7 cm
- Height (AB) = 24 cm

Substituting these values into the area formula:
\[ A = \frac{1}{2} \times 7 \times 24 \]

### Step 6: Perform the multiplication
Calculate:
\[ A = \frac{1}{2} \times 168 \]
\[ A = 84 \text{ cm}^2 \]

### Final Answer
The area of the right-angled triangle is \( 84 \text{ cm}^2 \).

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