Question

ratio of parimeter of two equilateral triangle is 5:9. find the ratio of their heights​

Answer 1

Answer:

$\red { Ratio \:of \: heights } \green { = \frac{5}{9}}$

Step-by-step explanation:

$Let \: x\: and\: X \:are \: sides \: of \: two \\equilateral \: triangles \: and \: h \: H \: are \\their \: corresponding \: heights \: respectively$

$Ratio \: of \: Perimeters = 5:9 \:(given)$

$\implies \frac{3x}{3X} = \frac{5}{9}$

$\implies \frac{x}{X} = \frac{5}{9} \:--(1)$

$Now, \:\frac{\frac{2h}{\sqrt{3}}}{\frac{2H}{\sqrt{3}}} = \frac{5}{9}$

$\boxed { \pink { side = \frac{2}{\sqrt{3}} \times height }}$

$\implies \frac{h}{H} = \frac{5}{9}$

Therefore.,

$\red { Ratio \:of \: heights } \green { = \frac{5}{9}}$

•••♪