A triangle has squares on its three sides as shown below. What is the value of x? Three squares having side lengths 6 cm, x cm,
1 answer:
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Answer:
Step-by-step explanation:
Consider triangles BKE and DKA. In this triangles:
as vertical angles;
as alternate interior angles (lines BC and AD are parallel and BC is a transversal);
as alternate interior angles (lines BC and AD are parallel and BE is a transversal).
Thus triangles BKE and DKA are similar by AA theorem. Similar triangles have proportional sides lengths:
Thus,
Since AD=BC and BC=BE+CE, we have that 4BE=BE+EC, EC=3BE. Hence, the ratio BE to EC is
