The perimeter of the parallelogram is 44 cm. The diagonal divides the parallelogram into two triangles.

| March 11, 2021 | education

The perimeter of the parallelogram is 44 cm. The diagonal divides the parallelogram into two triangles. The perimeter of each triangle is 30 cm. Find the length of the diagonal.

Let ABCE be the given parallelogram, BE the diagonal of the parallelogram.

Let us express the perimeter of the parallelogram:

P (ABCE) = AB + BC + CE + AE = 44 (cm).

Let’s express the perimeters of the triangles:

P (ABE) = AB + BE + AE = 30 (cm).

P (BCE) = BC + CE + BE = 30 (cm).

Add the perimeters of both triangles:

AB + BE + AE + BC + CE + BE = 30 + 30.

(BE + BE) + (AB + BC + CE + AE) = 60.

Since (AB + BC + CE + AE) is the perimeter of the parallelogram (= 44), the following equation is obtained:

2BE + 44 = 60.

2BE = 60 – 44.

2BE = 16.

BE = 8 (cm).

Answer: the length of the diagonal is 8 cm.



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