The area of an isosceles right-angled triangle ABC with a base of 50m squared. Height AH = 5√2 m.

The area of an isosceles right-angled triangle ABC with a base of 50m squared. Height AH = 5√2 m. What are the sides of the triangle?

We know the area of ​​an isosceles triangle and it is 50 m ^ 2, it is also known that the Height drawn to the base of BC AH = 5√2 m.

In order to find the sides, we first apply the formula to calculate the area of ​​a triangle and use it to find the base.

S = (BC * AH) / 2.

The area of ​​a triangle is half the height times the base. Substitute the known values ​​and find the base:

2 * 50 = BC * 5√2;

BC = 100 / 5√2;

BC = 10√2 m.

Consider a right-angled triangle formed by a height, half of the base equal to 5√2 cm and a side.

We are looking for the hypotenuse according to Comrade Pythagoras:

AC = √ ((BC / 2) ^ 2 + AH ^ 2) = √ (50 + 50) = √100 = 10 cm.

Answer: 10 cm, 10 cm and 10√2 cm.