The perimeter of a right-angled triangle is approximately 17 cm and the length of its hypotenuse is 7 cm.

The perimeter of a right-angled triangle is approximately 17 cm and the length of its hypotenuse is 7 cm. Calculate the area of the triangle if its legs are equal.

1. A, B, C – the vertices of a right-angled triangle. ∠С – straight. AB = 7 centimeters.

2. We calculate the length of the legs of the triangle using the formula for calculating its perimeter (P):

P = BC + AC + AB = 17 centimeters.

BC + AC = 17 – AB = 17 – 7 = 10 centimeters.

Considering that, according to the condition of the problem, the legs are equal, BC = AC = 10: 2 = 5 centimeters.

3. Calculate the area (S) of a given triangle:

S = AB x AC / 2 = 5 x 5/2 = 12.5 centimeters².

Answer: The area of a given triangle is 12.5 centimeters².