The legs of a right-angled triangle are 8 cm and 15 cm. Find the largest side of a triangle

The legs of a right-angled triangle are 8 cm and 15 cm. Find the largest side of a triangle with an area of 240 cm² similar to this one.

Determine the area of ​​the specified triangle.

To do this, we multiply its legs with each other and divide it into 2 parts.

8 * 15/2 = 120/2 = 60 cm2

We find how many times the area of ​​the second triangle is greater than the area of ​​the first.

240/60 = 4 times.

It follows from this that each of its legs is larger than the legs of the first triangle in:

√4 = 2 times.

Thus, the length of the legs of this triangle will be:

8 * 2 = 16 cm.

15 * 2 = 30 cm.

The largest side of a right-angled triangle is the hypotenuse, which is determined by the Pythagorean theorem.

c2 = 162 + 302 = 256 + 900 = 1156.

√1156 = 34 cm.

Answer:

34 cm.