A parallelogram has a 7 inch side and a 9 inch side, and the longer diagonal is 14 inches long. find the length of the other diagona. do you need a calculator

A parallelogram is a flat shape with opposite sides parallel and equal in length. The diagonals of a parallelogram bisect each other. In simpler words, they intersect halfway point. We calculate as follows:

d2 = √2a^2 + 2b^2 - d1^2
d2 = √2(7)^2 + 2(9)^2 - 14^2
d2 = 8 inches

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thaovtp1407 thaovtp1407 · Answer 2 · 2020-04-19T04:46:25+02:00

Answer:

the length of the other diagonal is ≈ 8

Step-by-step explanation:

Given that:

one side 7 inches
one side 9 inches
diagonal is 14 inches

we can use the law of cosines to find out the angle that formed by the 7 inch side and 9 inch side (please have a look at the attached photo)

Let say ∠ABC, we have:

[tex]c^{2} =a^{2} +b^{2} -2abcos(B)\\[/tex]

<=> [tex]14^{2} =7^{2} +9^{2} -2*7*9cos(B)\\[/tex]

<=> cos(B) = -11/21

<=> ∠ABC = 121 degrees.

From the properties of parallelograms, we know that the sum of the 4 inter angles is 360 degrees.

2∠ABC + 2∠BAC =360

<=> ∠BAC = (360 - 2∠ABC) /2

<=> ∠BAC = (360 - 2*121) /2

<=> ∠BAC =59 degrees

Once again, we use can use the law of cosines to find out the length of the shorter diagonal

[tex]d^{2} =a^{2} +b^{2} -2abcos(A)\\[/tex]

= [tex]7^{2} +9^{2} -2*7*9cos(59)\\[/tex]

= 65

<=> d = [tex]\sqrt{65}[/tex] ≈ 8