Answer:
3.14 cm
Explanation:
∆DEG is similar to ∆DFH, so
DE/DG = DF/DH
3.0/2.3 = (3.0 + 4.1)/(2.3 + x)
3.0/2.3 = 7.1/(2.3 + x) Divide each side by 7.1
2.3/3.0 = (2.3 + x)/7.1 Multiply each side by 7.1
(2.3 × 7.1)/3.0 = 2.3 + x Subtract 2.3 from each side
x = (2.3 ×7.1)/3.0 – 2.3
= 5.443 – 3.0
= 3.14 cm
Check:
3.0/2.3 = (3.0 + 4.1)/(2.3 + 3.14)
1.304 = 7.1 /5.44
1.304 = 1.305
The numbers check to the nearest hundredth.