Fifth gradeEE. 12 Area and perimeter: word problemsA rectangular sticker has an area of 10 square centimeters and a perimeter of 14centimeters. What are the dimensions of the sticker?
Accepted Solution
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Answer:Length = 5 cm, width = 2 cm.Step-by-step explanation:If L is the length and W the width we have the equations:LW = 10 <----- The area.2L + 2W = 14 <------ The perimeter.From the first equation L = 10/W so substituting for L in the second equation:2 * 10/W + 2W = 1420/W + 2W = 14 Multiplying through by W:20 + 2W^2 = 14W2W^2 - 14W + 20 = 0 Dividing by 2:W^2 - 7W + 10 = 0 (W - 5)(W - 2) = 0W = 5 or 2.So W is either 2 or 5 cm.Substituting W = 2 in LW = 10L * 2 = 10L = 5 cm.The length is longer than the width so the length is 5 cm and the width = 2 cm.