The sides (in cm) of a right triangle are (x − 18), (x − 25) and x. Its area (in cm²) is:

Correct option is D

Given:

The sides of a right triangle are (x - 18) cm, (x - 25) cm, and x cm.

Formula Used:

Pythagorean theorem:

​$$H^2 = P^2 + B^2$$​​

Area of a right triangle:

Area = $$\frac{1}{2} \times \text{Base} \times \text{Perpendicular}$$​​

Solution:

Using the Pythagorean theorem for this right triangle:

​$$x^2 = (x - 18)^2 + (x - 25)^2$$​​

​$$(x - 18)^2 = x^2 - 36x + 324$$​​

​$$(x - 25)^2 = x^2 - 50x + 625$$​​

​$$x^2 = (x^2 - 36x + 324) + (x^2 - 50x + 625)$$​​

​$$x^2 = 2x^2 - 86x + 949$$​​

​$$x^2 - 86x + 949 = 0$$​​

(x - 13)(x - 73) = 0

x = 13(not valid)

x = 73.

Now, 

If x=73x = 73:

Perpendicular: x - 18 = 73 - 18 = 55 cm

Base: x - 25 = 73 - 25 = 48 cm

Area  = $$\frac{1}{2} \times 48 \times 55 = 24 \times 55 = 1320 \, \text{cm}^2$$​​