Answer:
v = 60 yards
Step-by-step explanation:
In the similar triangles, their corresponding sides are proportional which means they have equal ratios
In triangles IHG and FHJ
∵ Δ IHG ≈ FHJ
∵ Side IH is corresponding to side FH
∵ Side HG is corresponding to side HJ
∵ Side IG is corresponding to side FJ
→ Their ratios are equal
∴ [tex]\frac{IH}{FH}[/tex] = [tex]\frac{HG}{HJ}[/tex] = [tex]\frac{IG}{FJ}[/tex]
∵ IH = 54 yards and FH = 72 yards
∵ IG = v and FJ = 80 yards
→ Substitute them in the first and last ratios above
∴ [tex]\frac{54}{72}[/tex] = [tex]\frac{v}{80}[/tex]
→ By using cross multiplication
∴ v × 72 = 80 × 54
∴ 72v = 4320
→ Divide both sides by 72
∴ v = 60 yards
