In the triangle <mi mathvariant="normal">&#x2220;<!-- ∠ --> A is right and D is a point on

Arraryeldergox2

Arraryeldergox2

Answered question

2022-06-13

In the triangle A is right and D is a point on the side AC such that the segments BD and DC have length equal to 1m. Let F be the point on the side BC so that AF is perpendicular to BC. If the segment FC measures 1m, determine the length of AC.
What´s the length of the segment AC in the triangle below?

Answer & Explanation

Blaine Foster

Blaine Foster

Beginner2022-06-14Added 33 answers

Step 1
Let E middle of BC. Then triangles DEC, AFC and BAC are similar. Then
C D E C = A C F C = B C A C = k
E C = C D k = 1 k , A C = k F C = k , B C = k A C = k 2
B C = 2 E C k 2 = 2 k k = 2 3
A C = k = 2 3
aligass2004yi

aligass2004yi

Beginner2022-06-15Added 7 answers

Step 1
We have:
c + m c + A D = c + A D c
So:
( c + A D ) 2 = c 2 + c m A D = c 2 + m c c
Therefore:
A C = c + A D = c 2 + m c

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