What is the area of the above right triangle, in terms of x?

Question

https://gmatclub.com/forum/download/file.php?id=43462 What is the area of the above right triangle, in terms of x? A. x^2/8 B. x^2/4 C. \frac{x^2\sqrt{2}}{2} D. x^2\sqrt{2} E. \frac{x^2\sqrt{2}}{4} image015.jpg

CounterSniper · Answer

The measure of the angles of the given triangle is surely 45:45:90
the ratio of sides of such triangle is 1:1: \sqrt{2}

now it is given that 
 \sqrt{2} *p = x (where p is the measure of each side)
p = x/ \sqrt{2}

area = \frac{b*h}{2}  = x/ \sqrt{2} * x/ \sqrt{2}  * 1/2 =  x^2 /4

shakav · Answer

as both sides of right angle triangle are equal
2*side^2=x^2
side^2=x^2/2

area of triangle=(1/2)*(side^2)
 =(1/2)*((x^2)/2)=(1/4)*(x^2)

venkivety · Answer

Angle 45 indicates that it is a isosceles right angle triangle in which the sides are in the ratio 1:1:√2
√2a= x
a= x/√2
area= 1/2bh
½ *(x/√2)* (x/√2)
Comes to x2/4

Abhishek009 · Answer

The given triangle is an isosceles right-angled triangle...

So,  a^2 + a^2 = x^2

Or,  2a^2 = x^2

Or,  a^2 = \frac{x^2}{2}

Since area of a triangle is  \frac{1}{2}*base*Altitude  =  \frac{x^2}{4} , Answer must be (B)

What is the area of the above right triangle, in terms of x?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

What is the area of the above right triangle, in terms of x?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards