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

August 29, 2021 | education

| **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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