Discussion
The perimeters of 5 squares are 24 cm, 32 cm, 40 cm, 76 cm and 80 cm respectively. The perimeter of another square equal in area to the sum of the area of these square is
Answer: C
Turn each perimeter into a side, square it, add, then work back.
\[ \text{sides} = \frac{24}{4},\; \frac{32}{4},\; \frac{40}{4},\; \frac{76}{4},\; \frac{80}{4} = 6,\; 8,\; 10,\; 19,\; 20 \]
\[ \text{total area} = 36 + 64 + 100 + 361 + 400 = 961 \text{ cm}^{2} \]
\[ \text{side of new square} = \sqrt{961} = 31 \text{ cm} \]
\[ \text{perimeter} = 4 \times 31 = 124 \text{ cm} \]
Perimeters do not simply add: their sum is 252 cm, twice the answer, because area grows with the square of the side.
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