*see attachement for diagram
Answer:
HG = 25.6
Explanation:
Given:
DE = 16x - 3
EF = 9x + 11
DF = 52
Required:
HG
SOLUTION:
✔️First, find the value of x
Thus, since DE is congruent to EF, therefore:
16x - 3 = 9x + 11
Collect like terms
16x - 9x = 3 + 11
7x = 14
Divide both sides by 7
x = 2
✔️Find EH:
Since diagonals of a rhombus are perpendicular, therefore ∆EHF is a right triangle.
Thus, we would use pythagorean theorem to find EH
EH² = EF² - HF²
EF = 9x + 11
Plug in the value of x
EF = 9(2) + 11 = 18 + 11
EF = 29
HF = 52/2 = 26 (diagonals bisect each other)
EH² = 29² - 26² = 165
EH = √165
EH = 12.8 (nearest tenth)
✔️Find HG:
HG = 2(EH) (diagonals bisect each other)
HG = 2(12.8)
HG = 25.6