How long and wide must a rectangle be, for its area to equal its perimeter? Assume the width and length are whole numbers.<\/p>\n
This is a nice little puzzle to let younger kids explore – if they find the puzzle as interesting or frustrating as I expect, they’ll remember the formulae for perimeter and area for the rest of their lives. For older kids, a bit of algebra gives the answer quickly.<\/p>\n
<\/p>\n
If the length is L and the width is W, and the perimeter equals the area, then LW = 2L+2W, so L = 2W \/ (W – 2). Pick a width, and this formula gives you the length. Trying a few different values of W, you’ll quickly find there’s only two rectangles with whole number sides, and area equal to perimeter – and one of them is a square.<\/p>\n
Well, if the kids are bored of this puzzle, you can try them on a second one – how long, wide and deep must a rectangular box be, for the volume to equal the surface area? Assume the length, width and depth are all whole numbers.<\/p>\n
Again, this can be done by trial and error, trying different rectangular boxes, and seeing what their surface area and volume are. Or, those with a bit of algebra can equate the formulae for surface area and volume, and try to find the dimensions of the box. It remains a more interesting puzzle, in ways, for two reasons<\/p>\n
For both these reasons, the puzzle is more open-ended – and that’s something that makes puzzles interesting.<\/p>\n
In case you need them, the formulae for the surface area and volume of a rectangular box are<\/p>\n
How long and wide must a rectangle be, for its area to equal its perimeter? Assume the width and length are whole numbers. This is a nice little puzzle to let younger kids explore – if they find the puzzle as interesting or frustrating as I expect, they’ll remember the formulae for perimeter and area … Continue reading Perimeter, Area and Volume<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[23,28,34,35,36,41,46],"_links":{"self":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts\/42"}],"collection":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/comments?post=42"}],"version-history":[{"count":1,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts\/42\/revisions"}],"predecessor-version":[{"id":1432,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts\/42\/revisions\/1432"}],"wp:attachment":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/media?parent=42"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/categories?post=42"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/tags?post=42"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}