Given an equilateral triangle ABC with each side 30cm. If xy is parellel to bc , xp is parellel to ac, yq is parellel to ab and xy+xp+yq=40cm, find pq.
Answers
Answer:
Step-by-step explanation:
If XY is parallel to BC , XP is parallel to AC and YQ is parallel to AB, this means that the triangle ΔXYP is an equilateral triangle too.
So, we can conlude that XP = XY = YP.
Let x be the measurement of the side of the triangle ΔXYP.
PQ = 3x - 40, (x is the measurement of the side of ΔXYP)
Then:
XY + XP + YQ = 40
⇒XY + XP + (YP - PQ) = 40
⇒x + x + x - PQ = 40
⇒ 3x - PQ = 40
⇒ PQ = 3x - 40
We know that the triangle ΔXYP has parallel sides to the triangle ΔABC and that it is equilateral, but we do not know the measurement of its sides.
Since we do not have information about the measurements of the sides of ΔXYP, we can generalize the measurement of PQ = 3x - 40.
If XY is parallel to BC , XP is parallel to AC and YQ is parallel to AB, this means that the triangle ΔXYP is an equilateral triangle too.
So, we can conlude that XP = XY = YP.
Let x be the measurement of the side of the triangle ΔXYP.
PQ = 3x - 40, (x is the measurement of the side of ΔXYP)
Then:
XY + XP + YQ = 40
⇒XY + XP + (YP - PQ) = 40
⇒x + x + x - PQ = 40
⇒ 3x - PQ = 40
⇒ PQ = 3x - 40
We know that the triangle ΔXYP has parallel sides to the triangle ΔABC and that it is equilateral, but we do not know the measurement of its sides.
Since we do not have information about the measurements of the sides of ΔXYP, we can generalize the measurement of PQ = 3x - 40