The shortest side of a rectangle is 18 units long and its diagonals measure 30 units. Find the area and perimeter of this rectangle.

Answer 1

As all four angles of a rectangle are right angles, we can create a right triangle using the short, long sides of the rectangle and the diagonal as the hypotenuse. If we let "x" represent the length of the longer side of the rectangle, we can create a couple of formulas for the area and perimeter of the rectangle:

A = L*W = (18)(x)

P = 2(L+W) = 2(x+18)

To find the longer side of the rectangle, x, we use the Pythagorean Theorem to calculate this value:

x² + 18² = 30²

x² + 324 = 900

x² = 576 --> x = 24

Therefore, the longest side of the rectangle is 24 units long. Therefore:

A = L*W = (18)(x) = (18)(24) = 432 square units

P = 2(L+W) = 2(x+18) = 2(24+18) = 2(42) = 84 units