One of the legs of a right-angled triangle is 4 times larger than the other, and its hypotenuse is √17. Find a larger leg.

Let one leg of the triangle be x, then the second leg will be 4x.
Now let’s recall the Pythagorean theorem: the sum of the squares of the legs is equal to the square of the hypotenuse.
In our case, this theorem will look like this:
x ^ 2 + (4x) ^ 2 = (√17) ^ 2
Having solved this equation, we find x – one leg.
x ^ 2 + 16x ^ 2 = 17
17x ^ 2 = 17
x ^ 2 = 17: 17
x ^ 2 = 1
x = 1
Now let’s find the second leg:
4 * 1 = 4 – the second leg of the right triangle.
4> 1
Answer: the larger leg of a right-angled triangle is 4.