The opposite sides of the rectangle are equal to each other, which means that the sum of two adjacent sides is equal to half of the perimeter:
a + b = P / 2;
a + b = 56/2 = 28 cm.
Let by condition a = 16 cm, then b = 28 – 16 = 12 cm.
The diagonal of a rectangle and two adjacent sides form a right-angled triangle, in which the diagonal is the hypotenuse, the sides are the legs. Therefore, by the Pythagorean theorem:
d ^ 2 = a ^ 2 + b ^ 2 = 16 ^ 2 + 12 ^ 2 = 256 + 144 = 400 = 202;
d = 20.
The diagonals of the rectangle are equal to each other, which means d1 = d2 = 20 cm.
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