the height of parallelogram is one third of it's base . if the area of

1.	the height of parallelogram is one third of it's base . if the area of the parallelogram is 192cm. find the height and base (4 marks)
Answer» Given : The height of PARALLELOGRAM is one THIRD of it's base. AREA of the parallelogram is 192 cm² To Find : Base of the parallelogram. Height of the parallelogram. Solution : LET the base of the parallelogram be x cm. Let the height of the parallelogram be y cm. Case 1 : The height of the parallelogram is ⅓ of the base. Equation : $\implies$ $\sf{height\:=\:\dfrac{1}{3}\:\times\:base}$ $\implies$ $\sf{y=\dfrac{1}{3}\:\times\:x}$ $\implies$ $\sf{y=\dfrac{x}{3}\:\:\:\:(1)}$ Case 2 : The area of the parallelogram is 192 cm². Formula : $\large{\boxed{\tt{Area_{parallelogram}\:=\:base\:\times\:height}}}$ Equation : $\implies$ $\sf{192\:=\:\:base\:\times\:height}$ $\implies$ $\sf{192\:=\:x\:\times\:y}$ $\implies$ $\sf{192\:=\:x\:\times\:\dfrac{x}{3}}$ $\bold{\big[From\:equation\:(1)\:y\:=\:\dfrac{x}{3}\big]}$ $\implies$ $\sf{192\:=\:\dfrac{x^2}{3}}$ $\implies$ $\sf{192\:\times\:3\:=\:x^2}$ $\implies$ $\sf{576=x^2}$ $\implies$ $\sf{\sqrt{576}\:=\:x}$ $\implies$ $\sf{24=x}$ Substitute, x = 24 in equation (1), $\implies$ $\sf{y=\dfrac{x}{3}}$ $\implies$ $\sf{y=\dfrac{24}{3}}$ $\implies$ $\sf{y=8}$ $\large{\boxed{\tt{\purple{Base\:of\:parallelogram\:=\:x\:=\:24\:cm}}}}$ $\large{\boxed{\tt{\purple{Height\:of\:parallelogram\:=\:y\:=\:8\:cm}}}}$