# In a rectangle with a perimeter of 16, the diagonals intersect at an angle of 90 degrees

In a rectangle with a perimeter of 16, the diagonals intersect at an angle of 90 degrees, which will be equal to the diagonal of the rectangle.

Let us denote the rectangle by the letters ABCD.

A rectangle whose diagonals intersect at an angle of 90 ° is a square.

By the condition of the problem, the perimeter (the sum of all sides) is 16 cm, in a square all sides are equal.

Let’s find the length of the side of the square:

P = 4 × AB;

AB = P: 4;

AB = 16: 4;

AB = 4 cm.

The diagonal of the square AC is the hypotenuse in the triangle ABC, where the legs AB = BC = 4 cm.

Let’s find the AS by the Pythagorean theorem:

AC ^ 2 = AB ^ 2 + BC ^ 2;

AC ^ 2 = 4 ^ 2 + 4 ^ 2;

AC ^ 2 = 16 + 16;

AC ^ 2 = 2 × 16;

AC = √ (2 × 16);

AC = 4√2 cm.

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