Question

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

Answer 1

The length of the other diagonal of the parallelogram is approximately 11.4 inches.

Step-by-step explanation:

To find the length of the other diagonal of the parallelogram, we can use the properties of parallelograms. In a parallelogram, the opposite sides are equal in length, so the length of the other side is also 9 inches. Now, we can use the Pythagorean theorem to find the length of the other diagonal. We have a right triangle with one side of length 7 inches, the other side of length 9 inches, and the hypotenuse of length 14 inches. Using the Pythagorean theorem, we can solve for the length of the other side:

a^2 + b^2 = c^2
7^2 + 9^2 = x^2
49 + 81 = x^2
130 = x^2
x = √130 ≈ 11.4 inches

Therefore, the length of the other diagonal is approximately 11.4 inches.

Answer 2

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 =
`√(65)` ≈ 8