question_answer 1)

A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side? Also find which shape encloses more area?

Answer:

                Perimeter of the rectangle \[=2\times (l+b)\]                                 \[=\text{2}\times (\text{4}0+\text{22})=\text{124 cm}\] \[\Rightarrow \]               Perimeter of the square \[=\text{124 cm}\] \[\Rightarrow \]         \[\text{4}\times \text{side}=\text{124}\] \[\Rightarrow \]               \[\text{side = }\frac{124}{4}\text{ cm}\] \[\Rightarrow \]               \[\text{= 31 cm}\] Hence, the measure of each side of the square is 31 cm. Area of the rectangle \[=l\times \text{b}\] \[=\text{4}0\times \text{22 c}{{\text{m}}^{\text{2}}}=\text{88}0\text{ c}{{\text{m}}^{\text{2}}}\] Area of the square \[=\text{side}\times \text{side}\] \[=\text{31}\times \text{31}=\text{961c}{{\text{m}}^{\text{2}}}.\]