Priya is making a rectangular banner for her school's National Day concert. The area of the banner is 96 cm² and its perimeter is 40 cm. There are two ways to label which dimension is the width and which is the length. Priya is told that the width of the banner must be more than 10 cm. What is the width of the banner?
Show Worked Solution
Worked Solution
Step 1: Use the perimeter to find the sum of the two sides.
2 x (length + width) = 40
length + width = 20 cm
Step 2: Use the area to find the product of the two sides.
length x width = 96 cm²
Step 3: Find two whole numbers that add to 20 and multiply to 96.
Test factor pairs of 96:
1 x 96 = 96 but 1 + 96 = 97
2 x 48 = 96 but 2 + 48 = 50
4 x 24 = 96 but 4 + 24 = 28
6 x 16 = 96 but 6 + 16 = 22
8 x 12 = 96 and 8 + 12 = 20
The two dimensions are 8 cm and 12 cm.
Step 4: Apply the constraint.
Width must be more than 10 cm, so width = 12 cm.
(8 cm fails the constraint since 8 < 10.)
Answer: 12 cm
Correct answer: 12 cm
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