Find the perimeter of a rectangular triangle in which the height drawn from the vertex

| June 22, 2021 | education

Find the perimeter of a rectangular triangle in which the height drawn from the vertex of the right angle divides the hypotenuse into segments of 9 and 16 cm.

Since CH is the height of a right-angled triangle drawn to the hypotenuse from the apex of the right angle, then CH ^ 2 = AH * BH = 16 * 9 = 144.

CH = 12 cm.

In a right-angled triangle BCH, according to the Pythagorean theorem, BC ^ 2 = CH^2 + BH^2 = 144 + 81 = 225.

BC = 15 cm.

The length of the hypotenuse AB = AH + BH = 16 + 9 = 25 cm.

In a right-angled triangle ABC, according to the Pythagorean theorem, AC ^ 2 = AB ^ 2 – BC ^ 2 = 625 – 225 = 400.

AC = 20 cm.

Let’s define the perimeter of the triangle ABC.

Ravs = AB + BC + AC = 25 + 15 + 20 = 60 cm.

Answer: The perimeter of the triangle is 60 cm.



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