A parallelogram has sides with lengths of #9 # and #8 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?

Question

A parallelogram has sides with lengths of #9  # and #8  #.  If the parallelogram's area is #36 #, what is the length of its longest diagonal?

Avery Allen · Accepted Answer

Longest diagonal = 15.4548

Area of parallelogram = l * h, where l is base and h is the corresponding height.

Evelyn Arboleda · Answer

undefined To find the length of the longest diagonal of the parallelogram, we can use the formula for the area of a parallelogram:

$$ \text{Area} = \text{base} \times \text{height} $$

Given that the area is 36 and one of the sides (base) is 8, we can find the height using the formula:

$$ \text{height} = \frac{\text{Area}}{\text{base}} $$

$$ \text{height} = \frac{36}{8} $$

$$ \text{height} = 4.5 $$

Now, since the longest diagonal divides the parallelogram into two congruent triangles, each with base 9 and height 4.5, we can use the Pythagorean theorem to find the length of the diagonal:

$$ \text{diagonal}^2 = \text{base}^2 + \text{height}^2 $$

$$ \text{diagonal}^2 = 9^2 + 4.5^2 $$

$$ \text{diagonal}^2 = 81 + 20.25 $$

$$ \text{diagonal}^2 = 101.25 $$

$$ \text{diagonal} = \sqrt{101.25} $$

$$ \text{diagonal} \approx 10.06 $$

So, the length of the longest diagonal of the parallelogram is approximately 10.06.