The sum of the hypotenuse AC and leg AB of the right-angled triangle ABC is 29, and their difference is 5 cm.

The sum of the hypotenuse AC and leg AB of the right-angled triangle ABC is 29, and their difference is 5 cm. Find the distance from the vertex A to the straight line BC.

let the hypotenuse – x, and the leg AB – y. their sum is 29, and the difference is 5.
{x + y = 29; x-y = 5
add 1 and 2 equation
2x = 34
x = 17 (hypotenuse)
17th = 5
y = 12 (leg AB)
answer: 12 cm