One side of the rectangle is 14 cm larger than the other. Find the sides of the rectangle if its diagonal is 26 cm.

One diagonal of the rectangle divides the rectangle into two equal right-angled triangles, in which it is the hypotenuse, the legs are the sides of the rectangle.

Let’s introduce a variable.

Let m be the width of the rectangle, (14 + m) the length of the rectangle. By the Pythagorean theorem, we get the equation:

m ^ 2 + (14 + m) ^ 2 = 676;

m ^ 2 + m ^ 2 + 28 * m + 196 – 676 = 0;

2 * m ^ 2 + 28 * m – 480 = 0;

m ^ 2 + 14 * m – 240 = 0;

Select the square of the binomial:

m ^ 2 + 14 * m + 49 – 289 = 0;

(m + 7) ^ 2 = 289;

m1 + 7 = -17;

m2 + 7 = 17;

m1 = -24 – doesn’t make sense.

m2 = 10.

Sides – 10 cm and 24 cm.