Applying the Pythagorean Theorem in the right-angled triangle ABC yields that the length of AD, the perpendicular from the right angle to the hypotenuse, is approximately 12.5 cm.
In a right-angled triangle ABC, where angle A is the right angle, and AD is perpendicular to BC, we can apply the Pythagorean Theorem to find the length of AD. The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (in this case, BC) is equal to the sum of the squares of the lengths of the other two sides.
Let AD be x. According to the theorem, BC squared is equal to AB squared plus AC squared. Since angle A is the right angle, BC squared is equal to BD squared plus DC squared.
Therefore, x squared is equal to 7.5 squared plus 10 squared. Solving for x, we get x is equal to the square root of 56.25 plus 100, which is approximately equal to the square root of 156.25, or roughly 12.5.
Hence, AD is approximately 12.5 cm. In this right-angled triangle, the length of AD, the altitude from the right angle to the hypotenuse, is found by applying the Pythagorean Theorem using the given values of BD and DC.
Complete question:
Triangle ABC is right-angled at A and AD is perpendicular to BC. If BD = 7.5 cm and DC = 10 cm, then what is AD equal to ?