An equivalent

An equilateral triangle has the same perimeter as a rectangle whose sides are b and h (b > h). Considering that the area of the triangle is three times the area of the rectangle. What is the value of b/h?

Correct answer:

r =  13.5145

Step-by-step explanation:

b=1 S1=b h=h S2=43 a2  o1=2b+2h=2+2h o2=3a=o1  3/4 a2=3h 3a=2+2h  3/4 (32+2h)2=3h  3/36 (2+2h)2=3h  k=3/360.0481  k(2+2h)2=3h  0.048112522432469 (2+2 h)2=3 h 0.19245h22.615h+0.192=0  a=0.19245;b=2.615;c=0.192 D=b24ac=2.615240.192450.192=6.6905989923 D>0  h1,2=2ab±D=0.38492.62±6.69 h1,2=6.7942318±6.7202369981503 h1=13.514468800022 h2=0.073994803720938   Factored form of the equation:  0.19245(h13.514468800022)(h0.073994803720938)=0  b>hh<1  h=h2=0.0740.074  r=b/h=1/0.074=13.5145

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Showing 1 comment:
Math student
If I good understand the task:
Let a=1 (Side of Triangel)
oT=3 (perimeter  of triangel)
ST=0,4330127... (Surface of Triangel)
SR=0,1433756...(Surface of  Rectangel)
h=SR/b (h=shorter side of Rectangel, b=longer side of Rectangel)
Then b2-1,5b+SR=0
and b=1,39665480...; h=0,10335451929... and b/h=r=13,51446313...
True-false test:
b*h=0,1033451929...*1,39665480...=0,14433756=ST/3
2*(b+h)=2*(1,39665480+0,1033451929)=3.





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