If possible, find the length of EF. If not, explain why the length of EF cannot be determined
1 answer:
9514 1404 393
Answer:
a. yes; AA similarity
b. maybe 8, (or 30)
Step-by-step explanation:
a. The missing angle of ∆ABC is 180° -60° -20° = 100°. So, two of the angles of ∆ABC match those of ∆DEF, meaning the triangles are similar by the AA theorem.
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b. We notice the side ratios to be ...
DE/AB = 12/9 = 4/3
Using that same ratio for corresponding sides ...
EF/BC = 4/3
EF = BC(4/3) = 6(4/3) = 8
Using the marked side lengths, we find EF = 8.
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We note that two angles and the side between them are sufficient information to solve ∆DEF with no reference to the markings of ∆ABC. Doing that, we find EF ≈ 30.4. We credit the discrepancy to the fact that ∆ABC is mis-marked. The longer side cannot be opposite the smaller angle.
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Question Correction
Evelyn packed this box with 1 inch cubes. Which expression does not show how Evelyn can find the volume of the box?
- (A)6+6+6+6+6+6
- (B) 2 X 3 X 6
- (C) 2 + 3 + 6
- (D) 6 X 6
Answer:
(C) 2 + 3 + 6
Step-By-Step Explanation
In the diagram,
- Height = 6 Units
- Length =2 Units
- Width =3 Units
Volume = Height X Length X Width
= 6 X 2 X 3
=36 cubic units
Consider the options:
(A)6+6+6+6+6+6 =36 cubic units
(B) 2 X 3 X 6 =36 cubic units
(C) 2 + 3 + 6 = 11 cubic units
(D) 6 X 6 =36 cubic units
Out of the option, that which is not equivalent to 36 cubic units is:
(C) 2+3+6
Therefore, it does not show how Evelyn can find the volume of the box.
