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KendallTishie724
22.10.2019 •
Mathematics
The width of a rectangle is 1 cm more than half the length. when both the length and width are increased by 1 cm, the area increases by 20 cm squared. find the original perimeter of the rectangle.
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Ответ:
38 cm.
Step-by-step explanation:
Let us assume that W and L are the width and length respectively of the given rectangle.
Hence, as the width of the rectangle is 1 more than half the length, so, we can write that,
W= 1+L/2, ⇒2W =2+L, ⇒ L=2W-2 (1)
Again, the given condition is that, if both L and W are increased by 1 cm, the area increases by 20 cm².
Hence, (W+1)(L+1) - WL =20, ⇒W+L =19 (2)
Now, solving equations (1) and (2) by substitution method, we get
W+(2W-2) =19, ⇒ 3W=21, ⇒W =7 cm.
Therefore, from equation (1), we get, L= 2W-2 =2×7-2=12 cm.
Hence, the original perimeter of the rectangle= 2(L+W) =2(7+12) =38 cm. (Answer)
Ответ:
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Step-by-step explanation:
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