If we know the area, we can first find the side length of this garden. The area of a square is the side length squared. So, we can write:
x^2 = 128
Square root both sides, and you get
x = sqrt (128)
The diagonal of the square is the side length times sqrt (2) because the diagonal plus two side lengths make a 45-45-90 triangle. So:
sqrt (128) * sqrt (2) = sqrt (256) = 16.
The length of the diagonal is 16 meters.
Answer with Step-by-step explanation:
Let s be the length of the side of the square garden
Then, Area=s²
The area of a square garden is 128 m²
i.e. s²=128 m²
s²=[tex](2^3)^2\times 2[/tex] m²
i.e. s= [tex]2^3\sqrt{2}\ m[/tex]
Also, the length of diagonal of a square is given by:
d= [tex]\sqrt{2}s[/tex]
= [tex]\sqrt{2}\times 2^3\times \sqrt{2}\ m[/tex]
= [tex]2^4\ m[/tex]
= 16 m
Hence, The length of diagonal of square garden is:
16 m
