Respuesta :
Answer:
Perimeter: [tex]48\sqrt{2} \: \mathrm{inches}[/tex]
Area: [tex]288\mathrm \: \mathrm{square \: inches}[/tex]
Step-by-step explanation:
If the diagonal of the square is 24 inches, the side length of the square is [tex]12\sqrt{2}[/tex] inches ([tex]2x^2=24^2[/tex]). The perimeter of this square is then [tex]4 \cdot 12\sqrt{2}=\fbox{$48\sqrt{2}\: \mathrm{in}$}[/tex] and the area [tex](12\sqrt{2})^2=\fbox{$288\: \mathrm{in^2}$}[/tex].
The area of the square is 288 in.² and the perimeter is 48√2 in.
Given to us,
Diagonal of the square = 24 in.
We know that for a square,
[tex]\bold{(Diagonal)^2 = 2\times (side)^2}[/tex]
substituting the values,
[tex]{(Diagonal)^2 = 2\times (side)^2}\\24^2 = 2\times (side)^2}\\side = 12\sqrt {2}[/tex]
Also, the area of a square is given by (side)², and, perimeter by (4 x side).
[tex]\bold{Area = (12\sqrt2)^2 = 288 in.^2}[/tex]
[tex]\bold{Perimeter= (4\times 12\sqrt2) = 48\sqrt 2 in.}[/tex]
Hence, the area of the square is 288 in.² and the perimeter is 48√2 in.
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