Two race cars,car x an y,are at the starting point of a two km track at the same time.car x and car y make one lap every 60 s an
d every 80 sec respectively.
How long, in minutes, will it take for the faster car to be 5 laps ahead of the slower car?
How long, in minutes, will it take for the faster car to be 5 laps ahead of the slower car?
1 answer:
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Answer: The length of segments between this point and the vertices of greater base are and 18.
Step-by-step explanation:
Let ABCD is the trapezoid, ( shown in below diagram)
In which AB is the greater base and AB = 18 DC= 11, AD= 3 and BC = 7
Let P is the point where The extended legs meet,
So, according to the question, we have to find out : AP and BP
In Δ APB and Δ DPC,
∠ DPC ≅ ∠APB ( reflexive)
∠ PDC ≅ ∠ PAB ( By alternative interior angle theorem)
And, ∠ PCD ≅ ∠ PBA ( By alternative interior angle theorem)
Therefore, By AAA similarity postulate,
Let, DP =x
⇒
⇒ 33 +11x = 18x
⇒ x = 33/7=
Thus, PD=
But, AP= PD + DA
AP=
Now, let PC =y,
⇒
⇒ 77 + 11y = 18y
⇒ y = 77/7 = 11
Thus, PC= 11
But, PB= PC + CB
PB= 11+7 = 18
<u>Answer-</u>
<em>The value of y is </em><em>6 units</em><em>.</em>
<u>Solution-</u>
Given ∆ABC ≅ ∆GEF
If two triangles are congruent, then the corresponding sides are also congruent.
So,
EF = BC, GF = AC
Putting the values,
--------------1
--------------------2
Putting the values of x in equation 1,
Therefore, the value of y is 6 units.