From the top of the right angle of a right-angled triangle with legs 6 cm and 8 cm, a perpendicular 12 cm

From the top of the right angle of a right-angled triangle with legs 6 cm and 8 cm, a perpendicular 12 cm long was drawn to find the distance from the end of this perpendicular to the middle of the hypotenuse.

Let us determine through what number of centimeters the length of the hypotenuse will be expressed, when from the condition of the task we know that the other two sides are equal to 6 and 8 centimeters, respectively:

√ (8 ^ 2 + 6 ^ 2) = √ (64 + 36) = √100 = 10.

Let us determine how many centimeters will be equal to half of the found hypotenuse:

10: 2 = 5.

Let us determine through what number of centimeters the length of a part of the hypotenuse, leg in a triangle, where the hypotenuse is equal to 8 cm, will be expressed:

√ (12 ^ 2 – 8 ^ 2) = √ (144 – 64) = √80 = 4√5.

Let’s define what the distance will be equal to:

4√5 – 5.

Answer: 4√5 – 5 cm.