Given: AB+BC=14cm AC+BD=20cm Formula: Perimeter of the rectangle =2(l+b) Rectangle has two equal diagonals. (Diagonal)2 = (Length)2 + (Breadth)2 Calculation: AC and BD are two diagonals of rectangle, then AC+BD=20 ⇒2AC=20[∵AC=BD] ⇒AC=20/2 ⇒AC=10 Let AB = x, then BC=(14–x) AC2=AB2+BC2 ⇒102=x2+(14–x)2 ⇒100=x2+196+x2–28x ⇒100=2x2+196–28x ⇒2x2–28x+96=0 ⇒x2–14x+48=0 ⇒x2–8x–6x+48=0 ⇒x(x–8)–6(x–8)=0 ⇒(x–6)(x–8)=0 Taking, (x–6)=0 ⇒x=6 (not in option) Taking, (x–8)=0 ⇒x=8 Hence, BC = 8 cm.