The sides (in cm) of a right triangle are (x − 13), (x − 26) and x. Its area (in cm²) is:

Correct option is B

Given:

Sides of right triangle: (x - 13), (x - 26), x cm

Formula Used:

Pythagoras Theorem: $$\text{Hypotenuse}^2 = \text{Base}^2 + \text{Height}^2$$​​

Area of right triangle: $$\text{Area} = \dfrac{1}{2} \times \text{Base} \times \text{Height}$$

Solution:
Apply Pythagoras:

​$$(x-13)^2+(x-26)^2=x^2 \\ \ \\x^2-26x+169+x^2-52x+676=x^2 \\ \ \\x^2-78x+845=0 \\ \ \\\Delta=78^2-4\times845=2704=52^2 \\ \ \\x=\frac{78\pm52}{2}\in{65,13}$$​​
Since x >26 (to keep x - 26 > 0, take x = 65).
Base x - 13 = 52 ,Height  x - 26 = 39.

Area $$=\dfrac{1}{2}\times 52\times 39=\dfrac{2028}{2}= 1014\ \text{cm}^2.$$​​