The perimeter of a right-angled triangle is 48 and the hypotenuse is 20, find its legs.

P = 48;

P = a + b + c; perimeter of a right triangle;

c = 20;

a + b + c = 48;

a + b + 20 = 48;

Let’s compose a system of equations:

{a + b = 28;

a ^ 2 + b ^ 2 = c ^ 2; by the Pythagorean theorem;

{a = 28 – b; let’s make a substitution;

(28 – b) ^ 2 + b ^ 2 = 20 ^ 2;

Let’s solve the second equation in the system:

784 – 56 * b + b ^ 2 + b ^ 2 – 400 = 0;

2 * b ^ 2 – 56 * b + 384 = 0;

b ^ 2 – 28 * b + 19 ^ 2 = 0;

D = 16;

b1 = 16;

b2 = 12;

We substitute the obtained values into the first equation of the system:

b1 = 16; a1 = 28 – 16 = 12;

b2 = 12; a2 = 28 – 12 = 16.