Maths-
General
Easy
Question
In the figure shown, BC is parallel to AD and AB =CD . What is the perimeter of quadrilateral ABCD?
The correct answer is: 56
HINT: Draw parallel lines, perpendicular to AD from B and C. Use Pythagoras theorem to find the sides.
Complete step by step solution:
Draw 2 perpendicular lines from B and C, and let these lines be BX and CY.
Since BC and AD are parallel, BX = CY = 6 units and also BX and CY are perpendicular to AD.
Hence, we can conclude that BC = XY = 10.
Consider ΔABX an ΔDCY
AB = CD (Given)
BX = CY (Since BC || AD)
(Perpendicular lines from B and C)
Therefore, 
(RHS congruence Rule)
Hence, AX = DY (CPCT)
From the figure, AX + XY + YD = 26
2AX + 10 = 26
2AX = 16
AX = 8
Thus, AX = 8 and YD = 8.
Now we have 2 congruent right angled triangles, ABX and DCY
We have AB2 = XB2 + AX2
AB2 = 62 + 82
AB2 = 100
AB = 10 [only positive value considered]
Given AB = CD, So CD =10
We have, AB = 10
BC = 10
CD = 10
AD = 26
Therefore, the total perimeter is 10 + 10 + 10 + 26 = 56 units.
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