The height drawn to the lateral side of the isosceles triangle is 15 cm and cuts off a segment 8 cm

| February 13, 2021 | education

The height drawn to the lateral side of the isosceles triangle is 15 cm and cuts off a segment 8 cm long on the lateral side, counting from the apex opposite the base. Find the area and perimeter of the triangle.

Since CH is the height, the triangle BCH is rectangular, in which, according to the Pythagorean theorem, we determine the length of the hypotenuse of the BC.

BC ^ 2 = BH ^ 2 + CH ^ 2 = 64 + 225 = 289.

BC = 17 cm.

Since the triangle ABC is isosceles, then AB = BC = 17 cm, then AH = AB – BH = 17 – 8 = 9 cm.

By the Pythagorean theorem, in the triangle ACН we determine the length of the hypotenuse AC.

AC ^ 2 = AH ^ 2 + CH ^ 2 = 81 + 225 = 306.

AC = 3 * √34 cm.

Let’s define the area of ​​the triangle ABC.

Savs = AB * CH / 2 = 17 * 15/2 = 127.5 cm2.

Let’s define the perimeter of the triangle ABC.

Ravs = 17 + 17 + 3 * √34 = 34 + 3 * √34 = √34 * (3 + √34) cm.

Answer: The area of ​​the triangle is 127.5 cm2, the perimeter is √34 * (3 + √34) cm.



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