Yes. The area of the triangle is .5(base*height). In a right triangle, the two legs are the base and the height. You can use the Pythagorean Theorem to find the lengths of the legs. Once you have the lengths of the legs, you can find the area.
So a is one leg, b is the other and b = 4a. And then you will have
a^2 + 4a^2 = 153
So just do the math and you have the lengths of the legs.
To determine the area of the triangle, you'll have to apply the formula of the area and not Pythagorean theorem.
Pythagora's theorem is applied only if you want to determine the cathetus of the triangle, in order to calculate the area.
The area of a right triangle is:
A = cathetus*cathetus/2
We'll note one cathetus by x and the other, 4x.
We'll apply the Pythagora's theorem:
x^2 + (4x)^2 = 153
x^2 + 16x^2 = 153
17x^2 = 153
We'll divide by 17:
x^2 = 9
x1 = 3 units (we'll accept only the positive value)
4*x1 = 4*3 = 12 units
Area = x*4x/2
Area = 2x^2
Area = 2*9
Area = 18 square units