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rainingsouls
24.06.2019 •
Mathematics
Along distance runner does a first lap around a track in exactly 50 seconds. as she tires, each subsequent lap takes 20% longer than the previous one . how long does she take to run three laps
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Ответ:
Please look at the steps below.
Step-by-step explanation:
1) m∠BAC=m∠CAD, m∠ACB=m∠ADC=90 degrees , then m<ABC=m∠ACD.
Therefore, triangles ADC and ACB are similary by AAA theorem.
2)AC /AB = AD/AC
3) Substituting the lengths, we get b/c = e/b
4) Cross multiplying the ratio, we get b^2 = ce
5) m∠ABC=m∠CBD, m∠ACB=m∠CDB=9, then m∠BAC=m∠BCD and the triangles BDC and BCA are similar by AAA theorem.
6) The ratio of the corresponding sides of similar triangles is in proportion.
BC/BD = AB/BC
7) Substituting the lengths, we get a/d = c/a
8) a^2 = cd
9) Add the results in 4) and 8), we get b^2 + a^2 = ce + cd
10) b^2 + a^2= c(e + d)
11) e + d =c, when we plug in step 10, we get a^2 + b^2 = c.c
a^2 + b^2 = c^2.
Hope this will helpful.
Thank you.