Farming And Mathing

Geometry Level pending

A rectangular shaped farm extent of 72 m 2 72 \text{ m}^2 . If the length is three time its width, find the length of the diagonal field in m m

6 2 6 \sqrt{2} 6 6 6 \sqrt{6} 6 15 6 \sqrt{15} 4 15 4 \sqrt{15} 4 30 4 \sqrt{30}

Jason Chrysoprase by Jason Chrysoprase , 18, Indonesia

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1 solution

Assume that p = p = length and l = l= width

p = 3 l p = 3l

p l = 72 pl = 72

3 l × l = 72 3l \times l = 72

3 l 2 = 72 3l^2 = 72

l = 24 l = \sqrt{24}

p = 3 l = 3 24 p=3l = 3 \sqrt{24}

Now find the diagonal

p 2 + l 2 \sqrt{p^2 + l^2}

= ( 3 24 ) 2 + ( 24 ) 2 = \sqrt{(3 \sqrt{24})^2 + (\sqrt{24})^2}

= 216 + 24 = \sqrt{216 + 24}

= 240 = \sqrt{240}

= 4 15 = 4 \sqrt{15}

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