Question

In right △DEF, the right angle is at E. Altitude EG¯¯¯¯¯ is drawn from E to the hypotenuse of △DEF dividing the hypotenuse into two segments. The hypotenuse of △DEF measures 20 inches, and EF=10.6 inches. What is the length of the longer segment of the hypotenuse of △DEF?

Answer 1

The length of the longer segment on the hypotenuse of right triangle DEF, given that the hypotenuse is 20 inches and one leg is 10.6 inches, is approximately 16.954 inches, or 16.95 inches when rounded to three significant figures.

Step-by-step explanation:

The student's question involves finding the length of a segment on the hypotenuse of a right triangle using Pythagorean theorem. We're given that triangle DEF is a right triangle with a right angle at E and that the hypotenuse DF, which is divided into two segments by altitude EG, measures 20 inches. Since EF is one leg of the triangle with a length of 10.6 inches and we need to find the length of the longer segment on the hypotenuse, we first identify the other leg, DE, using the Pythagorean theorem (DE2 + EF2 = DF2).

Let x represent the length of the segment ED. Then we have:

• x2 + (10.6 inches)2 = (20 inches)2
• x2 + 112.36 = 400
• x2 = 400 - 112.36
• x2 = 287.64
• x = √287.64
• x = 16.954 inches

Hence, the length of the longer segment on the hypotenuse is approximately 16.954 inches, or 16.95 inches when rounded to three significant figures.