geomatry

let ABC is the triangle with AC is Hypotenuse
area of this triangle = (1/2)*AB*BC

now the question is (1/2)*AB*BC>25??

Statement 1: let AB=6 since nothing is given about BC we can not determine confirmed area of triangle.
Therefore there is no way to determine whether the area of the triangle is greater than 25 or not.
for example: AB=6 BC=8 then area=24 < 25 hence ans NO
let AB=6 BC=10 then area = 30 >25 ans: Yes

Statement 2: now AB^2 + BC^2=10 given..........(A)
Area of triangle will be maximum if AB=BC

Put AB=BC in A then AB=BC=5√2

Therefore Maximum area would be 25. it is not greater than 25, because the maximum area is 25.

confirmed answer NO

Hence B

vipulgoyal wrote:is the area of a right angled trangle > 25 squre feet ??

1. one of the perpendicular sides is 6 feet
2. the largest side is 10 feet

B

Area = 1/2 * base * height

1. Base = 6
Not sufficient.

2. The largest side is always the hypotenuse.
base^2 + height^2 = 10^2
We cannot calculate the base and height from this information.
But if maximum of this product were less that or equal to 25*2, then this information would be sufficient.
To get the maximum, base = height
2*base^2 = 100
base^2 = 50
base = 5√2 = height
The maximum of this product is 50.
Sufficient.

Choose B

Cheers