PP1 (Shorter) Quant Section 2 (Medium) Q2

<p><span style="color:#8e44ad;"><span style="font-size:20px;">Deductions from the Given Information</span></span></p> <p>We can observe that there are two triangles here, $RSU$ and $TSU$.</p> <p><img alt="" src="https://gregmatapi.s3.amazonaws.com/media/misc/files/_class_pp1-shorter-quant-section-2-medium-q2.png" style="width: 400px; height: 218px;" /></p> <p>Firstly, we can work out that their bases are equal:</p> <ul> <li>$RS$ is the base of triangle $RSU$</li> <li>$ST$ is the base of triangle $TSU$</li> <li>Since we are told that $RS=ST$, we know that both triangles $RSU$ and $TSU$ have equal bases.</li> </ul> <p>Secondly, we can work out that their perpendicular heights are equal:</p> <ul> <li>The height of triangle $RSU$ is the perpendicular distance from the line $RS$ to the point $U$</li> <li>The height of triangle $TSU$ is the perpendicular distance from the line $ST$ to the point $U$</li> <li>We can see that the lines $RS$ and $ST$ are at the same vertical location, and point $U$ is also at a fixed vertical location.</li> <li>So, the heights of&nbsp;$RSU$ and&nbsp;$TSU$ must be the same.</li> </ul> <p>Finally, we can work out that their areas are equal:</p> <p>$Triangle\,Area = Base * Perpendicular\,Height$</p> <p>Since both $RSU$ and $TSU$ have the same base and perpendicular height, their areas are equal.</p> <p><span style="color:#27ae60;"><span style="font-size:20px;">Solving the Problem&nbsp;</span></span></p> <p>Since the two quantities we are told to compare are the areas of $RSU$ and $TSU$, which we have already calculated, we know that they are equal.</p> <p>So, the answer would be <span style="color:#27ae60;">C</span>.</p>