Question

the length of diagonal of a rombus are in the ratio 6:8 . if the perimeter is 40 cm .find the length of shorter diagonal

Answer 1

Perimeter of rhombus = 4 × side

40 = 4 × side

$\bf\huge\frac{40}{4}$ = side

10 = side

Pythagoras theorem

$(\frac{6p}{2})^2 + (\frac{8p}{2})^2 = (10)^2$

$\bf\huge 9p^2 + 16p^2 = 100$

$\bf\huge 25p^2 = 100$

$\bf\huge p^2$ = $\bf\huge\frac{100}{25}$

$\bf\huge p^2 = 4$

p = $\bf\huge\sqrt{4}$

p = 2 

Length of diagonal => 6 × 2 = 12cm

Hence Now  

8 × 2 = 16cm