Question

one of the diagonals of a rhombus is 15 cm and it's area is 150 cm . find the perimeter

Answer 1

we know that
$\frac{1}{2} \times d1 \times d2 = area$
so
$\frac{1}{2} \times 15 \times d2 = 150 \\ d2 = 150 \times \frac{2}{15} \\ d2 = 20$
now we know diagonal bisect each other so by Pythagoras theorem we have
$10 {}^{2} + (\frac{15}{2}) {}^{2} = x {}^{2}$
let side be x
$100 + \frac{225}{4} = x {}^{2}$
$\frac{400 + 225}{4} = x {}^{2} \\ \frac{625}{4} = x {}^{2} \\ x = \sqrt{ \frac{625}{4} } \\ x = \frac{25}{2}$
now perimeter is side *4
$= \frac{25}{4} \times 4 \\ = 25$
25cm is the answer

Answer 2

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