For what value of x is BC || HK
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In the figure, AC = 3, CE = x, and BC is parallel to DE. If the area of triangle ABC is 1/12 of the area of triangle ADE, then x = ?
Another useful property: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: AREAarea=S2s2AREAarea=S2s2.
Next, note that ABC and ADE are similar triangles, thus the ratio of their areas is the square of the ratio of their sides: AE2AC2=121AE2AC2=121 --> AEAC=12−−√=23√AEAC=12=23 --> AE=23√∗AC=63√AE=23∗AC=63 --> x=AE−AC=63√−3x=AE−AC=63−3.
Another useful property: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: AREAarea=S2s2AREAarea=S2s2.
Next, note that ABC and ADE are similar triangles, thus the ratio of their areas is the square of the ratio of their sides: AE2AC2=121AE2AC2=121 --> AEAC=12−−√=23√AEAC=12=23 --> AE=23√∗AC=63√AE=23∗AC=63 --> x=AE−AC=63√−3x=AE−AC=63−3.
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