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

August 28, 2021 | education

| 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.

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