The legs of a right triangle are 12 cm and 16 cm. Find the perimeter of a triangle like this one if its area is 24 cm2.

1. Vertices of a triangle A, B, C. BC = 12 cm. AC = 16 cm. Vertices of a similar triangle M, K, E.

2. Calculate the area of ​​a given triangle:

S = BC x AC / 2 = 12 x 16: 2 = 96 cm².

3. Calculate the coefficient of similarity of triangles (k)

k² = S triangle ABC / S triangle MKE = 96: 24 = 4.

k = √4 = 2.

4. We calculate the lengths of the legs ME and KE:

AC / ME = 2.

ME = 16: 2 = 8 cm.

BE / KE = 2.

KE = 12: 2 = 6 cm.

5. We calculate the length of the MK hypotenuse:

MK = √KE² + ME² = √6² + 8² = √36 + 64 = √100 = 10 cm.

6. Calculate the perimeter (P) of the MKE triangle:

P = 10 + 6 + 8 = 24 cm.

Answer: The perimeter of the MKE triangle similar to the ABC triangle is 24 cm.