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w8u, 91h, e3, i9, 長方形の辺の長さ | 熊野塾

熊野塾

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長方形の辺の長さ

2020年1月30日 塾長からの挑戦状

大きさの違う長方形Aと長方形Bを2つずつ使ってL字型に組み合わせると,上の図のようになりました。このとき,長方形Aと長方形Bのたてとよこの長さはそれぞれ何cmでしょうか?

長方形を知っていれば小学校低学年でも十分解けますが,大人でも苦戦するかも?

答えと解説は下の方へ

【答え】

長方形Aは26cmと6cm,長方形Bは20cmと6cm

【解説】

長方形Aの長い辺をX,短い辺をx,長方形Bの長い辺をY,短い辺をyとします。

下の長方形Aのすぐ上に,長方形Bの長い辺と長方形Aの短い辺が乗っているので,

Y+x=X …①

です。また,右の長方形Aのすぐ左に長方形Bの長い辺と短い辺がくっついているので,

Y+y=X …②

です。

①と②を比べると,Y+x=Y+y であることが分かります。つまりx=yです。

図を見ると,x+y=12 なので,x=y=6 です。

また,X+x=32なので X=26 です。

あとは①か②よりY=20 であることが分かります。

 

文字を使っているので「なんや,数学やん!」と思った方もいたかも知れませんが,「Bの長い辺とAの短い辺の和が,Bの長い辺と短い辺の和と同じだから…」と考えると,それほど数学っぽい話ではありません。でも,図を見ているだけでは意外と気づけないものですよね。文字式で表すと,図で見ただけでは気づきにくいものも簡単に見抜くことができるという効果があるんですね。