Question

Type the correct answer in the box. Use numerals instead of words. In parallelogram DEFG, DE = 6 inches and DF = 6.4 inches. Diagonals GE and DF intersect at point H. If GH = 4 inches, what is the length of GE?

GE = _______ inches

Answer 1

In parallelogram DEFG, DE = 6 inches, DF = 6.4 inches, and GH = 4 inches. To find the length of GE, we can use the Pythagorean Theorem to find FH and then subtract FH from DE to obtain GE. The length of GE is approximately 1.2 inches.

Step-by-step explanation:

In parallelogram DEFG, diagonal GE intersects diagonal DF at point H. Given DE = 6 inches, DF = 6.4 inches, and GH = 4 inches, we need to find the length of GE. Since GH divides DF into two equal segments, FH and HD, we can use the Pythagorean Theorem to find the length of FH. FH^2 + GH^2 = DF^2.

Plugging in the values, we get FH^2 + 4^2 = 6.4^2. Solving for FH, we get FH ≈ 4.8 inches.

Since GE extends from H to the other endpoint of DE, we can find the length of GE by subtracting FH from DE. GE = DE - FH = 6 - 4.8 = 1.2 inches.

Therefore, the length of GE is approximately 1.2 inches.