The two sides of the triangle are equal to each other, and the third side of the triangle is 2 cm larger

| February 18, 2021 | education

The two sides of the triangle are equal to each other, and the third side of the triangle is 2 cm larger than each of them. The area of the square built on the larger side of the triangle is 36 cm2. Find the area of a rectangle built on the smaller side of the triangle if one of the sides of the rectangle is 2 times larger than its other side. Consider different cases.

Since the area of ​​the square built on the larger side of the triangle is 36 cm², the larger side of the triangle is √36 = 6 cm. The larger side in this triangle is the base.

If the large side of the triangle is 2 cm larger than the other side, then the second (and third) side is 6 – 2 = 4 cm.

On this side, a rectangle is built, the sides of which differ by two times.

Suppose that 4 cm is the large side, then the smaller side of the rectangle will be 2 cm, the area is: S = 4 * 2 = 8 cm².

Suppose that 4 cm is the smaller side, then the larger side is 8 cm, the area will be 4 * 8 = 32 cm².

Answer: the area of ​​the rectangle is 8 cm² or 32 cm².



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