Respuesta :
The polygon with greater area is the square and that with greater perimeter is the rectangle, this is so because the length of sides of the square differ from that of the rectangle
How to determine the parameters
From the information given, we have that:
- Diagonal of rectangle and square is 52cm
- Side of the rectangle is 20cm
Formula for perimeter of a rectangle
Perimeter = [tex]2l + 2 \sqrt{d^2 - l^2}[/tex]
Perimeter = 2( 20) + 2 [tex]\sqrt{52^2 - 20^2}[/tex]
Perimeter = 40 + 2 ( 48)
Perimeter = 136 cm
Perimeter of a square = 2 √2d
Perimeter = 2 √ 2(52)
Perimeter = 2√104
Perimeter = 20. 3 cm
Area of square = 1/2 diagonal square
Area = 1/ 2 × 52²
Area = 1352 cm²
Area of rectangle = [tex]l\sqrt{d^2 - l^2}[/tex]
Area = 20 [tex]\sqrt{52^2 - 20^2}[/tex]
Area = 20 × 48
Area = 960cm²
Thus, the polygon with greater area is the square and that with greater perimeter is the rectangle, this is so because the length of sides of the square differ from that of the rectangle
Learn more about polygons here:
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