Question

Find the perimeter of the rectangle whose length of one side is 12 cm and the length of the diagonal is 13 cm.

• A. 34 cm
• B. 60 cm
• C. 120 cm
• D. 50 cm

Answer 1

The correct option is A

34 cm

For calculating the perimeter of rectangle, we require both length and breadth.

Perimeter = 2(length + breadth)

From the figure given,
AB = CD = 12 cm

△BCD is right angled at C.

So, by using Pythagoras' theorem,

${BC}^2$ + ${DC}^2$ = ${BD}^2$
Hence, ${BC}^2$ = ${BD}^2$ - ${DC}^2$

Now, BD = 13 cm, DC = 12 cm

So, ${BC}^2$ = ${13}^2$ - ${12}^2$
⇒ ${BC}^2$ = 25 ${cm}^2$
⇒ $BC$ = 5 cm

Hence, the breadth of the rectangle is 5 cm.

So, perimeter = 2(length + breadth)
= 2(BC + DC)
= 2(5 + 12)
= 2×17
= 34 cm