Question

If ELF is congruent to GJH, EF=12 and LF=7.8 find IJ. Round answer to the hundredths place. A. 4.78 B 5.62 C 4.98 D 5.07

Answer 1

EF = 12

KF = 6

LF = 7.8

LK = sqrt(7.8^2-6^2) = 4.98

IJ = LK

Answer 2

Answer with explanation:

→ΔELF ≅ Δ GHJ-------[Given]

→EF=GH----------[CPCT]

→GJ=FL-------[CPCT]

Let , O be the center of the circle.

→ EK=KF--------[Perpendicular from the center to the chord bisects the chord.]

→GI=IH------[Reason same as Above]

→→EK=GI, KF=HI

→→OJ=OL

→OK=KI

→OJ-OK=OL-KI

→LK=IJ

⇒→Δ LKF ≅ Δ JIG-------[SAS]

Now, In Δ LKF, By Pythagorean Theorem

→(LF)²=(LK)²+(KF)²

→(7.8)²=(LK)²+(6)²

→60.84-36=(LK)²

→24.84=(LK)²

LK=4.98

→→LK=IJ=4.98

Option C:→4.98