Question

Find the value of each variable in the parallelogram. Please show work, if possible!

Answer 1

In a parallelogram, the shorter diagonal represents the sum of the vectors, and the longer diagonal represents the difference of the vectors.

Step-by-step explanation:

For parts (a) and (b), we attach the origin of vector B to the origin of vector A, as shown in Figure 2.14, and construct a parallelogram. The shorter diagonal of this parallelogram is the sum A + B. The longer of the diagonals is the difference A - B. We use a ruler to measure the lengths of the diagonals, and a protractor to measure the angles with the horizontal. For the resultant R, we obtain R = 5.8 cm and OR ≈ 0°. For the difference Ď, we obtain D = 16.2 cm and Op : 49.3°, which are shown in Figure 2.14.

Answer 2

Given:

The diagonals of the parallelogram bisect each other.

Thus, the lengths of the diagonals of the parallelogram are (k + 4), 11, m and 8.

We need to determine the value of the variables k and m.

Value of k:

Since, we know that, the diagonals bisect each other which means that the diagonals cut each other into two equal halves.

Thus, we have;

`k+4=11`

`k=7`

Thus, the value of k is 7.

Value of m:

Applying the same property that diagonals bisect each other. We have;

`m=8`

Thus, the value of m is 8.

Hence, the value of the variables k and m are 7 and 8 respectively.