### Video Transcript

If the ratio of ๐ฅ to ๐ฆ to ๐ง is
three : four : eight, then what is the value of ๐ฅ squared plus ๐ฆ squared plus ๐ง
squared divided by ๐ฆ multiplied by ๐ฅ plus ๐ง.

We can see from the ratio given
that our value of ๐ฅ is equal to three, our value of ๐ฆ is equal to four, and our
value of ๐ง is equal to eight. We can substitute these values
directly into our expression. Three squared is equal to nine,
four squared is 16, and eight squared is 64. So the numerator simplifies to nine
plus 16 plus 64. We can simplify the denominator by
using our order of operations known as PEMDAS or BIDMAS. We do the parentheses or brackets
first, leaving us with four multiplied by 11. Nine plus 16 plus 64 is equal to
89. Four multiplied by 11 is 44.

The value of the expression ๐ฅ
squared plus ๐ฆ squared plus ๐ง squared divided by ๐ฆ multiplied by ๐ฅ plus ๐ง is 89
over 44. This fraction can not be simplified
as 89 and 44 have no common factor apart from one.