In △ABC, point D∈AC
1 answer:
<h3>Answer:</h3>
- ABDC = 6 in²
- AABD = 8 in²
- AABC = 14 in²
A diagram can be helpful.
When triangles have the same altitude, their areas are proportional to their base lengths.
The altitude from D to line BC is the same for triangles BDC and EDC. The base lengths of these triangles have the ratio ...
... BC : EC = (1+5) : 5 = 6 : 5
so ABDC will be 6/5 times AEDC.
... ABDC = (6/5)×(5 in²)
... ABDC = 6 in²
_____
The altitude from B to line AC is the same for triangles BDC and BDA, so their areas are proportional to their base lengths. That is ...
... AABD : ABDC = AD : DC = 4 : 3
so AABD will be 4/3 times ABDC.
... AABD = (4/3)×(6 in²)
... AABD = 8 in²
_____
Of course, AABC is the sum of the areas of the triangles that make it up:
... AABC = AABD + ABDC = 8 in² + 6 in²
... AABC = 14 in²
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Answer:
(x) =
Step-by-step explanation:
Let y = f(x) and rearrange making x the subject
y = 5 - 2x ( add 2x to both sides )
2x + y = 5 ( subtract y from both sides )
2x = 5 - y ( divide both sides by 2 )
x =
Change y back into terms of x
(x) =