Re: In the above figure AB = 6 and BC = 8
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08 Mar 2025, 13:56
As the measure of angle $x$ is not known, a unique value of the area of triangle cannot be found. Case 1 - If angle x is obtuse i.e. greater than 90 degrees.
In the given figure, a perpendicular AD is drawn from A to BC .
The area of a triangle is $\(\frac{1}{2} \times\)$ Base $\(\times\)$ Height, where in triangle $A B C$ base is 8 and the height is
AD.
Next in triangle ADB , the hypotenuse i.e. AB is 6 units long, so the length of the perpendicular i.e. AD must be less than 6 .
So, if we assume $\(\mathrm{AD}=6\)$, the area of the triangle ABC must be less than $\(\frac{1}{2} \times 8 \times 6=24\)$
Case 2 - If we assume that angle x is 90 degrees
Now, the area of the triangle ABC is $\(\frac{1}{2} \times\)$ Base $\times$ Height $\(=\frac{1}{2} \times 8 \times 6=24\)$
Similarly if we consider case 3 in which the measure of angle $\(x\)$ is less than 90 , we would get the area of triangle ABC greater than 24.
Hence a unique comparison cannot be formed between column A \& column B quantities, so the answer is (D).