question_answer

Mrs Kaushik gives a problem to her students. Find the perimeter of a rectangle whose length is 28 cm and diagonal is 35 cm. What will be the correct answer?

A)                      90 cm                        

B)  45 cm

C)         89 cm            

D)         98 cm

Correct Answer: D

Solution :

ABCD is a rectangle, In \[\Delta \,ACB,\] \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\] (By Pythagoras theorem) \[{{(35)}^{2}}={{(28)}^{2}}+B{{C}^{2}}\] or  \[B{{C}^{2}}={{(35)}^{2}}-{{(28)}^{2}}\] \[\Rightarrow \] \[B{{C}^{2}}=1225-784\Rightarrow B{{C}^{2}}=441\] \[\therefore \] \[BC=\sqrt{441}=21\,cm\] \[\therefore \] Perimeter of rectangle \[=2\times (28+21)\,cm\] \[=2\times (49)\,cm=98\,cm\]