Question

a parallelogram has sides of length units and units. the shorter diagonal is units. find the measure of the longer diagonal.

Answer 1

To find the measure of the longer diagonal of a parallelogram with given side lengths and a shorter diagonal, use the formula (1/2) * sqrt(2 * x^2 + 2 * y^2 - z^2), where x, y, and z represent the lengths. Substitute the given lengths into the formula to find the measure of the longer diagonal.

Step-by-step explanation:

A parallelogram with sides of length x units and y units and a shorter diagonal of z units can be represented using the formula:

(1/2) * sqrt(2 * x^2 + 2 * y^2 - z^2)

In this case, the measure of the longer diagonal would be the value obtained by substituting the given lengths into the formula.

For example, if x = 4 units, y = 6 units, and z = 5 units:

(1/2) * sqrt(2 * 4^2 + 2 * 6^2 - 5^2)

= (1/2) * sqrt( 32 + 72 - 25)

= (1/2) * sqrt( 79)

= approximately 5.6 units

Answer 2

The value of the longer diagonal is 26.33 unit

Using the concept of pythagoras :

• 
  `a^(2) + b^(2) = c^(2)`

`c^(2) = (19 + 10)^(2)`

`c^(2) = 729`

Now we can find the length of the longer diagonal ;

b² = c² - a²

b² = 729 - 36

b² = 693

b = √693

b ≈ 26.33

Complete Question:

A parallelogram has sides of length 19 units and 10 units. The shorter diagonal is 12 units. Find the measure of the longer diagonal.