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

Answer Link

thaovtp1407 thaovtp1407 · Answer 2 · 2020-04-18T22:46:25-04:00

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:

\(c^{2} =a^{2} +b^{2} -2abcos(B)\\\)

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

<=> 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

\(d^{2} =a^{2} +b^{2} -2abcos(A)\\\)

= \(7^{2} +9^{2} -2*7*9cos(59)\\\)

= 65

<=> d = \(\sqrt{65}\) ≈ 8