The perimeter of parallelogram abcd is equal to 10 cm. find the length of diagonal bd if you know that the perimeter of △abd is 8 cm.

The length of the diagonal BD is 3 centimeters.

A parallelogram is a quadrilateral where each pair of parallel sides have the same length and can be form by two congruent triangles which share the same side (diagonal).

Perimeter equations for the parallelogram are the following:

(1)

(2)

Where:

By (2) we have the following conclusion:

And we find the length of the diagonal BD by (1):

The length of the diagonal BD is 3 centimeters.

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we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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-1/2 +2

step-by-step explanation: