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Find the area of rhombus whose …

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Find the area of rhombus whose perimeter is 100m and one of whose diagonal is 30m

Posted by Kashish Taank 8 years, 3 months ago

CBSE > Class 09 > Mathematics

3 answers

Sneha Sneha 8 years, 3 months ago

So now, area of rhombus = 1/2* d1*d2 therefore, 1/2*30*40= 600sq cm

Sneha Sneha 8 years, 3 months ago

Firstly, we know that all sides of a rhombus are equal therefore it's perimeter = 100m so, it's one side = 100/4=25m one diagnol = 30m =30/2 =15m so by pythagorus theorem,we have =20m second diagnol = 2*20 =40m

Naveen Sharma 8 years, 3 months ago

Perimeter of Rhombus = 100 m
Side of Rhombus = {tex}{100\over 4}= 25 m {/tex}

One diagonal of Rhombus (d₁) = 30 m
Second diagonal of rhombus = d₂

As we know, diagonal of rhombus bisect each other at 90 degree. So,
{tex}d_1^2+d_2^2= 4(side)^2\\ =>900 + d_2^2 = 4\times 625\\ => d_2^2 = 2500-900=1600\\ => d_2 = 40{/tex}

Area of rhombus = {tex}{1\over 2}\times d_1\times d_2\\ = {1\over 2}\times 30\times 40 \\ = 600 m^2{/tex}

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