In a right-angled triangle, a height of 12 cm long is drawn to the hypotenuse and divides

In a right-angled triangle, a height of 12 cm long is drawn to the hypotenuse and divides it into segments with a difference of 7 cm between them. Find a pyrimeter

1.∠С = 90 °. CE – height. P is the perimeter of ΔABС.

2. Let’s say AE – BE = 7 cm.

3. Take the length of AE as x. Length BE = x – 7.

4. Let’s compose the equation:

x (x – 7) = 12²;

x² – 7x – 144 = 0;

The first value x = (7 + √49 + 576) / 2 = (7 + √625) / 2 = (7 + 25) / 2 = 16 cm.

The second value x = (7 – 25) / 2 = – 9 cm – is not accepted.

AE = 16 cm. BE = 16 – 7 = 9 cm.

5.AB = 9 + 16 = 25 cm.

6. AC = √AE² + CE² = √256 + 144 = 20 cm.

7. BC = √BE² + CE² = √81 + 144 = 15 cm.

8.Р = 20 + 15 + 25 = 60 cm.

Answer: P = 60 cm.