The side of the rectangle refers to its diagonal as 21:29 and the other side is 100. Find the area of the rectangle.

The diagonal of a rectangle is the hypotenuse of the formed right triangles. By the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the legs. Let us express the unknown sides in terms of x and compose the equation:

21x – rectangle leg;

29x – hypotenuse;

21x² + 100² = 29x²;

8x² = 100²;

8x² = 10000;

x² = 10000/8;

x² = 1250;

x = √1250;

x = 35.4;

21x = 21 * 35.4 = 742.5 cm – side of the rectangle.

Now let’s find the area of a rectangle by multiplying its sides:

S = 100 * 742.5;

S = 74,250 cm².