Given that,

The altitude of a right triangle is 7 cm less than its base.

So, let's assume that

The base of right-angle triangle is x cm.

So,

Altitude of right-angle triangle is x - 7 cm.

Thus, we have In right angle triangle

Base = x cm

Altitude = x - 7 cm

Hypotenuse = 13 cm

Now, By using Pythagoras Theorem , we have

Base²+Altitude² = Hypotenuse²

So, on substituting the values, we get

x² + (x-7)² = 13²

x² + x² + 49 - 14x = 169

2x² + 49 - 14x = 169

2x² + 49 - 14x - 169 = 0

2x² - 14x - 120 = 0

2(x² - 7x - 60) = 0

x² - 7x - 60 = 0

x(x - 12) + 5(x - 12) = 0

(x - 12)(x + 5) = 0

x = 12 or x = -5 (not possible)

So,

Base of right-angle triangle = 12 cm

Altitude of right angle triangle = 12 - 7 = 5 cm