AGHJ ~ ACDE. GH = 5 yards, HJ = 7.5 yards, CD = 9 yards. What is the length of DE?
To find the length of DE, we need to find the length of AG first and then subtract the length of AC from it.
As given, GH = 5 yards and HJ = 7.5 yards.
Therefore, GH + HJ = 5 + 7.5 = 12.5 yards.
Now, we are given that AGHJ ~ ACDE (meaning they are similar).
Using the property of similar triangles, we can write the ratio of corresponding side lengths as:
AG / AC = GH / CD
Substituting the given values, we get:
AG / AC = 5 / 9
Cross multiplying, we get:
AG = 5 / 9 * AC
Given that AG + AC = 12.5 yards, we can substitute AG in terms of AC:
5 / 9 * AC + AC = 12.5
Combining like terms:
14 / 9 * AC = 12.5
Dividing both sides by 14 / 9:
AC = 12.5 / (14 / 9) = 11.7857 yards (rounded to four decimal places)
Now, to find the length of DE, we can subtract AC from AG:
DE = AG - AC = 12.5 - 11.7857 = 0.7143 yards (rounded to four decimal places)
Therefore, the length of DE is approximately 0.7143 yards.