In a triangle, the two sides are equal and each side is 3 times the third side of the triangle.

In a triangle, the two sides are equal and each side is 3 times the third side of the triangle. The perimeter of this triangle is 28 cm. Find the area of a rectangle built on the side of the triangle if the perimeter of the rectangle is equal to the perimeter of the triangle.

1. Vertices of the triangle A, B, C. AB = BC.

2. We take the length of the AC side as x (cm). Then AB = BC = 3x cm.

3. Draw up an equation using the formula for calculating the perimeter of a triangle (P).

P = x + 3x + 3x.

7x = 28.

x = 4 cm.

The length of the speaker side is 4 cm.

4. If the rectangle is built on the AC side, then one of its sides is 4 cm.

5. We calculate the length of the other side of the rectangle, taking it for x cm. To do this

we use the formula for calculating the perimeter of a rectangle, which, according to the condition of the problem

equal to the perimeter of the triangle (28 cm):

2 x 4 + 2x = 28;

2x = 20;

x = 10 cm.

6. Calculate the area (S) of the rectangle:

S = 4 x 10 = 40 cm².

Answer: the area of ​​the rectangle built on the AC side of the ABC triangle is 40 cm².