The perimeter of an isosceles triangle is 98 and the side is 25. Find the area
1) The perimeter of a triangle is the sum of all its sides. Since in an isosceles triangle, the two sides are equal, the perimeter is found by the formula P = AC + 2 * AB.
The area of a triangle is equal to half the product of the base and the height drawn to it (S = 1/2 * a * h).
2) So, to find the area of the triangle, you need to draw the height BH. Then the area of the triangle ABC will be found by the formula: S = 1/2 * BH * AC.
3) Knowing that the perimeter of the triangle is 98, the side is 25, we find the side AC.
AC + 2 * AB = 98;
AC + 2 * 25 = 98;
AC + 50 = 98;
AC = 98 – 50;
AC = 48.
4) Find the height BH. To do this, consider a right-angled triangle ABH (∠ BHA = 90 °): AB = 25; AH = 1/2 * AC = 1/2 * 48 = 24 it is carried out, in half).
5) According to the Pythagorean theorem in a right-angled triangle, the sum of the hypotenuse is equal to the sum of the squares of the legs. In a right-angled triangle ABH, this theorem can be represented as follows: AB² = BH² + AH².
25² = BH² + 24²;
BH² = 25² – 24²;
BH² = 625-576;
BH² = 49;
BH = ± √49
BH = ± 7
Because – 7 does not satisfy the condition of the problem, BH = 7.
6) Find the area of triangle ABC.
S = 1/2 * BH * AC;
S = 1/2 * 7 * 48;
S = 168.
Answer: 168.
