Question

Triangle ABC ~ triangle DEF. Use the image to answer the question.

a triangle ABC with side AC labeled 7.93 and a second triangle DEF with side DE labeled 8.8, side FD labeled 6.1 and side EF labeled 6.4

Determine the length of side AB and BC in triangle ABC.

Answer 1

Can you provide more information about triangle ABC

Explanation:

Based on the information provided, it is not possible to determine the lengths of sides AB and BC in triangle ABC. To determine the lengths of the sides of a triangle, you need to know either all three sides, two sides and the included angle, or one side and two angles. In this case, we only know one side of triangle ABC (AC = 7.93), which is not enough information to determine the lengths of the other two sides

Answer 2

AB = 11.44 , BC = 8.32

Explanation:

Since the triangles are similar , then the ratios of corresponding sides are in proportion, that is

`(AB)/(DE)` =
`(AC)/(DF)` ( substitute values )

`(AB)/(8.8)` =
`(7.93)/(6.1)` ( cross multiply )

6.1 × AB = 8.8 × 7.93 = 69.784 ( divide both sides by 8.8 )

AB = 11.44

and

`(BC)/(EF)` =
`(AC)/(DF)` ( substitute values )

`(BC)/(6.4)` =
`(7.93)/(6.1)` ( cross multiply )

6.1 × BC = 6.4 × 7.93 = 50.752 ( divide both sides by 6.1 )

BC = 8.32