The lateral side of an isosceles triangle is 17 cm, and the bisector drawn to the base is 15 cm.

The lateral side of an isosceles triangle is 17 cm, and the bisector drawn to the base is 15 cm. Find the area and perimeter of this triangle.

The area of ​​a triangle is found by the formula:

S = 1/2 * a * h, that is, one second of the product of the base and the height.

According to the condition, our triangle is isosceles, which means that the bisector drawn to the base is both the height and the median, which means that the height of our triangle is h = 15 cm.

Our isosceles triangle is the bisector, the median and the same height divides into two identical right-angled triangles, in which the hypotenuses are the sides, and the leg is the height.

By the Pythagorean theorem, you can find the second leg of a right triangle, that is, half the base.

It will be equal to the square root of the difference between the squares of the numbers 17 and 15:

a / 2 = √ 172 – 152 = √ 64 = 8 cm.

Then the base of our isosceles triangle will be 16.

a = 8 * 2 = 16 cm (by the property of the median of an isosceles triangle).

We substitute the found values ​​of the height and base into the formula for the area of ​​a triangle:

S = 1/2 * a * h = 1/2 * 15 * 16 = 120 cm2.

To find the perimeter of a triangle, you need to add all its sides:

P = 17 cm + 17 cm + 16 cm = 50 cm.

Answer: the area is 120 cm2, and the perimeter is 50 cm.