Question

The lenghth of the diagonals of arombus are 12cm and 16cm.calculate the perimeter of the rombus

Answer 1

Step-by-step explanation:

let ABCD be a rhombus

AC and BD are diagonal.

diagonals intersect at O.

in a rhombus diagonal bisects each other and are perpendicular

diagonal are 12 cm and 16 cm

AOB is a right angle triangle formed

here AO = a = 6cm,

BO = b = 8cm and AB = c

${a}^{2} + {b}^{2} = {c}^{2} \\ {6}^{2} + {8}^{2} \div {c}^{2} \\ 36 + 64 = {c}^{2} {c}^{2} = 100 \\ c = \sqrt{100} = 10$

Therefore AB = 10cm

all sides of rhombus are equal

AB = BC = CD = AD = 10cm

perimeter of rhombus is sum of all sides

10 + 10 + 10 + 10 = 40cm