Triangle PQR and triangle PRC are right-angled isosceles triangles in rectangle ABCD.
AP = 5cm and AQ = 3cm.
Find the length of AD.
Answer
10 cm
Solution
Additional lines are drawn as in the figure below.
△ APQ and△ EQR are congruent.
As AP = EQ = 5cm and AQ = ER = 3cm, AE = FR = 3 + 5 = 8 cm and FP = 5 - 3 = 2 cm.
Next, △ FPR and△ GRC are congruent.
FP = GR = 2cm and FR = GC = 8cm.
Therefore AD = FG = 8 +2 = 10 cm.
