An equilateral triangle with side length 9 cm is shown in the diagram, work out the area of the triangle.
1 answer:
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Answer: The answer is x = 6 units.
Step-by-step explanation: Please refer to the attached diagram
The diagram in the question shows two triangles placed on each other and for convenience sake has been labelled ABDCE. Triangle ABC is a right angled triangle, and so is triangle ADE. From the marks on the lines, we can infer that line AD is equal in measurement to line DB. Also line AE is equal in measurement to line EC.
Therefore we can see the similarity in both triangles, if AD and AE equals DB and EC, then it follows that DE equals BC.
Hence if AD = DB and
AE = EC, and
DE = BC
Then, x - 3 = ½x
(½x can also be expressed as x/2)
x - 3 = x/2
By cross multiplication we now have
2(x - 3) = x
2x - 6 = x
By collecting like terms we now have
2x - x = 6
x = 6
