A Region of land 50meters by 40meters is to cross diagonally by a road 15meters wide. What is the roads area?
we start by calculating the value of x
152=x2+x215^2=x^2+x^2152=x2+x2
225=2x2225=2x^2225=2x2
225/2=x2225/2=x^2225/2=x2
112.5=x2112.5=x^2112.5=x2
112.5=x2\sqrt{112.5}= \sqrt{x^2}112.5=x2
10.61=x10.61=x10.61=x
length x= 10.61m
next we find the diagonal D
length = 50−x=50−10.61=39.3950-x=50-10.61=39.3950−x=50−10.61=39.39
width =40−x=40−10.61=29.3940-x=40-10.61=29.3940−x=40−10.61=29.39
D=39.392+29.392\sqrt{39.39^2+29.39^2}39.392+29.392
D=49.1549.1549.15
area of the road =15∗D15*D15∗D
=15∗49.1515*49.1515∗49.15
=737.25m2737.25m^2737.25m2
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