The legs of a right-angled triangle are 3: 4 and the hypotenuse is 50 mm find the segments into which the hypotenuse

The legs of a right-angled triangle are 3: 4 and the hypotenuse is 50 mm find the segments into which the hypotenuse is divided by the height drawn from the vertex of the right angle

Let the smaller leg be 3a.

Then, in accordance with the conditions, the larger one can be expressed using 4a.

Since we know that the hypotenuse is 50 mm, we can write down the equation and find out the length of each leg:

(3a) ^ 2 + (4a) ^ 2 = 50 ^ 2;

25a ^ 2 = 2500;

a ^ 2 = 100;

a1 = 10;

a2 = -10 (not suitable);

3 * 10 = 30;

4 * 10 = 40.

Let’s find out what is the length of the required segments:

30 = √ (50 * x);

900 = 50x;

x = 18;

50 – 18 = 32.

Answer: The first segment will be equal to 18 centimeters, and the other segment will be equal to 32 centimeters.