Let the points $\left(\frac{11}2,\alpha\right)$ lie on or inside the triangle with sides $x+y=11$, $x+2y=16$ and $2x+3y=29$. Then the product of the smallest and the largest values of $\alpha$ is equal to :

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] The vertices are $(6,5)$, $(4,7)$, $(10,3)$. The line $x=5.5$ meets the side $x+y=11$ at $y=5.5$ and the side $2x+3y=29$ at $y=6$ (it does not meet $x+2y=16$ within the triangle). So $5.5\le\alpha\le6$ and the product is $5.5	imes6=33$. Answer (3).

Q. Let the points $\left(\frac{11}2,\alpha\right)$ lie on or inside the triangle with sides $x+y=11$, $x+2y=16$ and $2x+3y=29$. Then the product of the smallest and the largest values of $\alpha$ is equal to :

Explanation

Reviewed by Dr. Abubacker

Want to attempt the full paper?