PP1 (Shorter) Quant Section 2 (Hard) Q4

<p><span style="color:#8e44ad;"><span style="font-size:20px;">Deductions from the Given Information</span></span></p> <p>We can sketch the points $R$ and $T$ on the coordinate grid like this. We can notice that the line $RT$ is opposite a right angle at the origin, so we can use the Pythagorean Theorem to calculate the length of side $RT$.</p> <p><img alt="" src="https://gregmatapi.s3.amazonaws.com/media/misc/files/class_pp1-shorter-quant-section-2-tough-q4.png" style="width: 300px; height: 252px;" /></p> <p>$RT = \sqrt{2^2+1^2} = \sqrt{5}$</p> <p>We also know that since $RST$ is an equilateral triangle, each side will have the same length. So we have three sides, each with length $\sqrt{5}$.</p> <p><span style="color:#27ae60;"><span style="font-size:20px;">Solving the Problem</span></span></p> <p>We only need to calculate QA here. Based on our deductions above, the perimeter of $RST$ would be $3\sqrt{5}$, which is the same as QB.</p> <p>So, the answer must be <span style="color:#27ae60;">C</span>.</p>