<p>How do I solve these? Has anybody seen a question similar (to the first) in the past?</p>
<p>Sorry if these have been previously asked :/</p>
<ol>
<li><p>8 sqrt(8) can be re-written as 16 sqrt(2), or 4 sqrt(32), or 2 sqrt(128). Different (x,y) values are (16,2), (4,32), (2,128) - pick any one. If you choose (16,2), for example, x+y = 18.</p></li>
<li><p>Area of a triangle = 0.5(height)(base), and triangle RQS has half the height and base of the outer triangle RPT. Trapezoid RQST has an area = area of RPT- area of RQS
= area(RPT) - 0.25 area(RPT)
= 0.75 area(RPT)</p></li>
</ol>
<p>Thanks a lot, optimizerdad!</p>
<p>1.
8 sqrt(8) = x sqrt(y)
From the look of it x=8 and y=8 is one possible solution.
x+y=16 is one possible answer.</p>
<p>2.
Mark the middle of PT as point M and connect it to the points Q and S.
Triangles QRS, PQM, QMS, and MST have equal areas (their heights and bases are respectively equal), each of them 1/4 of the area of the triangle PRT.
PQST consists of three such triangles, therefore its area is 3/4 of the areaof the triangle PRT.</p>
<p>For the first question, x and y must be different positive integers.</p>
<p>Sorry! My bad.
Would this make it up?
8 sqrt(8) = x sqrt(y)
2^9 = x^2 y
2^2 2^7 = x^2 y
One possible answer:
x=2
y=2^7=128</p>
<p>For the first one I rewrote it as sqrt(8x64), and you can simplify that out to various stages. </p>
<p>Although, I suppose rewriting it as 16sqrt(2) immediately would be the faster method :).</p>
<p>Math Curve = sharp and harsh</p>