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In drilling world's deepest hole it was found that the temperature $T$ in degree celcius, $x$ km below the earth's surface was given by $T=30+25(x-3), 3 \leq x \leq 15$. At what depth will the temperature be between $155^{\circ} \mathrm{C}$ and $205^{\circ} \mathrm{C}$ ?
Solution:
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Verified Answer
Let the length of shortest side be $x \mathrm{~cm}$.
According to the question
Longest side $=2 \times$ Shortest side $=(2 x) \mathrm{cm}$
and thrd side $=2+$ Shortest side $=(2+x) \mathrm{cm}$
Perimeter of triangle $=x+2 x+(x+2)=4 x+2$
Since, Perimeter $>166 \mathrm{~cm}$
$$
\Rightarrow 4 x+2>166 \Rightarrow 4 x>166-2
$$
$\Rightarrow 4 x>164 \therefore x>\frac{164}{4}=41 \mathrm{~cm}$
Hence, the minimim length of shortest side is $41 \mathrm{~cm}$.
According to the question
Longest side $=2 \times$ Shortest side $=(2 x) \mathrm{cm}$
and thrd side $=2+$ Shortest side $=(2+x) \mathrm{cm}$
Perimeter of triangle $=x+2 x+(x+2)=4 x+2$
Since, Perimeter $>166 \mathrm{~cm}$
$$
\Rightarrow 4 x+2>166 \Rightarrow 4 x>166-2
$$
$\Rightarrow 4 x>164 \therefore x>\frac{164}{4}=41 \mathrm{~cm}$
Hence, the minimim length of shortest side is $41 \mathrm{~cm}$.
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