One of the sides of the rectangle is two centimeters smaller than the other, and its diagonal is 10 cm

| August 17, 2021 | education

One of the sides of the rectangle is two centimeters smaller than the other, and its diagonal is 10 cm, find the perimeter of the rectangle.

1. In the calculations we will use the Pythagorean theorem: the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the legs.

2. According to the problem statement, the length of the diagonal of the rectangle is 10 cm.

Let’s designate the side as x cm, then the length of the second side will be expressed as (x – 2) cm.

Let’s make the equation

x² + (x – 2) ² = 10²;

x² + x² – 4 x + 4 – 100 = 0;

2 x² – 4 x – 96 = 0;

x = (4 + √16 + 4 * 96 * 2) 4 = (4 + √ 16 + 768): 4 = (4 + 28): 4 = 8.

The second side is 8 cm – 2 cm = 6 cm.

3. Calculate the perimeter of the rectangle

2 * (8 cm + 6 cm) = 28 cm.

Answer: The perimeter is 28 cm.



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