Question

Geometry

The diagonals of a  kite are in the ratio of 3:2. The area of the kite is 27 cm^2 .  Find the length of both diagonals. (Hint: Let the lengths of the diagonals be 3x and 2x)

How do I do this?

Answer 1

`A=27 \ cm^2 \\ \\ d_(1)=3x , \ \ d_(2) = 2x \\ \\ S=(1)/(2)\cdot d_(1)\cdot d_(2)\\ \\27 = (1)/(2)\cdot 3x \cdot 2x \\ \\ 3x^2 = 27 \ \ /:3`


`x^2 = 9 \\ \\3x=x=√(9)\\ \\x=3 \ cm \\ \\ d_(1)=3x = 3*3 =9 \ cm \\ \\d_(2)=2x=2*3 = 6 \ cm \\ \\ Answer : \\ The \ length \ of \ the \ diagonal \ is: \ d_(1)= 9 \ cm \ and \ d_(2)= 6 \ cm`