<p>Does anyone remember how to solve this problem? I can't seem to figure it out:</p>
<p>A picnic shelter in a park will cover a square region 30 ft. by 30 ft. (900 square ft.). The park has dimensions 60 ft. by 150 ft. If you want to build the picnic shelter using only a portion of the this space, 40 ft. by 130 ft., how many different locations in the park are possible for the placement of the picnic shelter? </p>
<p>There is an accompanying small sketch with the problem: 1 rectangle that is 60 x 150 and the bordering edge along each side of the rectangle is shaded (the area that you cannot build the shelter in) and the 2nd rectangle (unshaded) within the the first rectangle.</p>
<p>I'm not sure how to obtain the answer which is 22.</p>
<p>Ok, I looked at [Area</a> problem using counting](<a href=“Math Forums | Math Help Forum”>Math Forums | Math Help Forum) and sort of understood the answer.</p>
<p>I’m guessing the shelter must be along the edges of the interior space (40x130). Combining the answer and the other guy’s response, I’m also assuming you move the shelter down by 10 feet (not 1 like the other guy indicated). Perhaps they got this number from the 10 foot boundary around the park dimensions? I’m not sure. But that’s the only way to get 22.</p>
<p>Personally, I would assume that there would be 10 x 100 ways, because I would think that the shelter could be anywhere within the 40 x 130 space.</p>
<p>Forget about the exterior space and focus only on the 40 x 130 rectangle which the 30 x 30 shelter must fit in. First look at how many times you can put the edge (30 ft) on the 130 ft border. You can see that this is 11 (from the shelter’s edge starting all the wat in the corner to thirty feet from the far edge). Doing the same with the 40 ft border, its obvious that there are only two ways to postion the shelter (along each opposite edge). We therefore have 2 sets of 11 possibilities, or 2 * 11 = 22 total locations.</p>
<p>I know this may be very difficult to visualize or follow, but using the picture can really help.</p>
<p>@Greywolf i had the same exact reasoning during the test</p>