In parallelogram ABCD, the AC diagonal is perpendicular to the CD side. Find the perimeter of triangle ACD

| June 2, 2021 | education

In parallelogram ABCD, the AC diagonal is perpendicular to the CD side. Find the perimeter of triangle ACD if the sides of the parallelogram are 8 cm and 15 cm.

A parallelogram is a quadrilateral in which opposite sides are equal and lie on parallel lines.

Since the AC diagonal is perpendicular to the CD side, it divides the parallelogram into two right-angled triangles.

Consider a triangle ΔАСD.

The perimeter of a triangle is the sum of all its sides.

In order to find the perimeter of the triangle ΔАСD, you need to calculate the length of the AC side. Since this triangle is rectangular, we will use the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AD ^ 2 = AC ^ 2 + DC ^ 2;

AC ^ 2 = AD ^ 2 – DC ^ 2;

AC ^ 2 = 15 ^ 2 – 8 ^ 2 = 225 – 64 = 161;

AC = √161 = 12.69 cm.

PACD = AC + DC + AD;

PACD = 15 + 8 + 12.69 = 35.69 cm.

Answer: the perimeter of the triangle ΔАСD is 35.69 cm.



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