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 measuring 7 inches and 8 inches. What is the length of this altitude of △DEF

Answer 1

To find the length of the altitude EG in right triangle DEF, we can use the similar triangles formed by EGD and EFB. By setting up a proportion and solving for EG, we find that EG is equal to 3.5 inches.

Step-by-step explanation:

In right triangle DEF, the altitude EG is drawn from E to the hypotenuse DF.

The hypotenuse is divided into two segments measuring 7 inches and 8 inches.

We can use the similar triangles formed by EGD and EFB to find the length of EG.

Since the triangles are similar, we can set up a proportion: EG/ED = FB/EF. Substituting the given values, we have EG/(7 inches) = 8 inches/(7 inches + 8 inches).

Simplifying the proportion and solving for EG, we get EG = (7 inches * 8 inches) / (7 inches + 8 inches) = 3.5 inches.

Answer 2

The length of altitude EG in triangle DEF is 7 inches.

Step-by-step explanation:

The length of altitude EG is 7 inches.

To find the length of altitude EG of triangle DEF, we need to use similar triangles. Since EG is an altitude, it is perpendicular to the hypotenuse of DEF. This means that EG divides the hypotenuse into two segments that are proportional to the corresponding sides of the triangle. Since the two segments have lengths of 7 inches and 8 inches, the length of altitude EG is equal to the ratio of the 7-inch segment to the hypotenuse multiplied by the length of the hypotenuse. So, the length of altitude EG is 7 inches.