Find the diagonals of the rectangle if its length and width are equal: a) 5 cm and 12 cm b) 6 cm and 8 cm.

The diagonal divides the rectangle into two right-angled triangles and is the hypotenuse of the resulting right-angled triangle.

Therefore, knowing the two sides of the rectangle, which, respectively, are the legs of the resulting triangle, you can find the diagonal (hypotenuse) by the Pythagorean theorem:

a ^ 2 + b ^ 2 = c ^ 2. where a, b – legs (sides of the rectangle), c – hypotenuse (diagonal).

c = √ (a ^ 2 + b ^ 2).

Means:

a) c = √ (5 ^ 2 + 12 ^ 2) = √ (25 + 144) = √169 = 13.

b) c = √ (6 ^ 2 + 8 ^ 2) = √ (36 + 64) = √100 = 10.