# The area of a triangle is 52 cm2 larger than the area of a similar triangle. The perimeter of the smaller triangle refers

July 29, 2021 | education

| **The area of a triangle is 52 cm2 larger than the area of a similar triangle. The perimeter of the smaller triangle refers to the perimeter of the larger triangle as 6: 7. Determine the area of the smaller of these triangles.**

We are given two triangles that are similar to each other.

It is also known that the area of one triangle is 52 cm ^ 2 larger than the area of the second triangle.

Let’s start by writing down the area of the second triangle:

S2 = S1 + 52,

Perimeters are 6: 7:

P1 / P2 = 6/7.

It is known that in such triangles the areas are referred to as squares of similar sides (in our case, the perimeters.

Writes the ratio:

S1 / S2 = P1 ^ 2 / P2 ^ 2,

S1 / (S1 + 52) = 36/49;

S1 = 144 cm ^ 2, S2 = 169 cm ^ 2.

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