The base and the altitude of a right-angled triangle are 15 cm and 8 cm respectively. What is the altitude from the opposite vertex to its hypotenuse?

Correct option is C

Given:

Base of the right-angled triangle = 15 cm

Altitude (height) of the right-angled triangle = 8 cm

Formula Used:

Area $$= \frac{1}{2} \times \text{base} \times \text{height}$$​

Solution:

Let the hypotenuse be h and the altitude from the opposite vertex to the hypotenuse be h_a.

Using the Pythagorean theorem to find the hypotenuse:

​$$h^2 = \text{base}^2 + \text{height}^2 = 15^2 + 8^2 = 225 + 64 = 289$$​​

​$$h = \sqrt{289} = 17 \, \text{cm}$$​​

​$$\text{Area} = \frac{1}{2} \times \text{hypotenuse} \times \text{altitude} = \frac{1}{2} \times 17 \times h_a$$​​

​$$\frac{1}{2} \times 15 \times 8 = \frac{1}{2} \times 17 \times h_a$$​​

60 $$= \frac{17}{2} \times h_a$$​

120 = 1$$7 \times h_a$$​

​$$h_a = \frac{120}{17} \approx 7\frac {1}{17} \, \text{cm}$$ 
Alternate Method: 
Altitude from the opposite vertex to the hypotenuse = $$\frac{P\times B}{H} = \frac{15\times8}{17} = 7 \frac{1}{17 } \text{cm}$$​​