Answer:
The height is 12√2
Step-by-step explanation:
Area of a parallelogram = base × height
From the question
Area = 8√90
base = 2√5
Substitute the values into the above formula and solve for the height
That's
[tex]8 \sqrt{90} = 2 \sqrt{5} h \\ h = \frac{8 \sqrt{90} }{2 \sqrt{5} } \\ h = \frac{24 \sqrt{10} }{2 \sqrt{5} } [/tex]
Reduce the fraction with 2
That's
[tex]h = \frac{12 \sqrt{10} }{ \sqrt{5} } [/tex]
Split √10
We have
[tex]h = \frac{12 \sqrt{2} \times \sqrt{5} }{ \sqrt{5} } [/tex]
Reduce the fraction with√5
We have the final answer as
12√2
Hope this helps you
