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In triangle \(ABC\), side \(AB\) is 5 inches and side \(BC\)

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Source: — Data Sufficiency |
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by deloitte247 » Sat Oct 05, 2019 8:23 pm
Side AB = 5 inches
Side Bc = 7 inches
Area of the triangle = 1/2 * base * height
= (base * height)/2
So, what is the area of Triangle ABC?
Statement 1: Angle ABC is 90 degrees.
This means that triangle ABC is a right angle triangle in which angle B = 90 degrees.
$$If\ B=90^0$$
Then base = AB and height = BC; hypotenuse = AC
Or
Base = BC and height = AB; hypotenuse = AC
$$Therefore,\ Area=\frac{AB\cdot BC}{2}or\ \frac{BC\cdot AB}{2}$$
$$Therefore,\ Area=\frac{5\cdot7}{2}or\ \frac{7\cdot5}{2}$$ $$Therefore,\ Area=17.5inches^2\ each.\ $$
Statement 1 is SUFFICIENT.

Statement 2: Triangle ABC is a right angle triangle.
This means that either of A, B or C = 90 degrees
$$If\ \angle A=90^0,\ then\ base\ and\ height\ =\ AB\ and\ AC\ or\ AC\ and\ AB$$
$$If\ \angle B=90^0,\ then\ base\ and\ height\ =\ AB\ and\ BC\ or\ BC\ and\ AB$$
$$If\ \angle C=90^0,\ then\ base\ and\ height\ =\ AC\ and\ BC\ or\ BC\ and\ AC$$
Since, we don't have the definite angle, we cannot find the area of triangle ABC, so, statement 2 is NOT SUFFICIENT.
Since, statement 1 alone is SUFFICIENT, then Answer = option A.

Thanks
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