In a rectangular trapezoid ABCD, the bases are 17 inches and 40 inches, and the height CD is 25 inches.

| March 5, 2021 | education

In a rectangular trapezoid ABCD, the bases are 17 inches and 40 inches, and the height CD is 25 inches. Find the sum of the diagonals of the trapezoid.

Since the trapezoid is rectangular, the triangles BCD and ACD are also rectangular.

According to the Pythagorean theorem, from the right-angled triangle ACD we determine the length of the hypotenuse AC.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 40 ^ 2 + 25 ^ 2 = 1600 + 625 = 2225.

AC = 5 * √89 cm.

In a right-angled triangle ВСD, we define, according to the Pythagorean theorem, the hypotenuse ВD.

BD ^ 2 = BC ^ 2 + CD ^ 2 = 17 ^ 2 + 25 ^ 2 = 269 + 625 = 914.

ВD = √914 cm.

Let us determine the sum of the lengths of the diagonals of the trapezoid.

АС + ВD = 5 * √89 + √914 cm.

Answer: The sum of the diagonals of the trapezoid is 5 * √89 + √914 cm.



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