A wire of length 200 cm is cut into 2 parts & each part is bent to form a square.
If the area of the larger square is 9 times that of the smaller square, find the perimeter of the larger square.
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The wire of length L is cut in to two lengths, L1 and L2. They are bent into two squares with sidelengths of s1 and s2. Note that each side s of a square is equal in length, so
L = L1 + L2 = 4*s1 + 4*s2 = 200 cm.
Area = length x width = s1 * s1 or s2 * s2, so
A1 = s1^2 and A2 = s2^2
Since A1 = 9A2 and A1 = s1^2
A1 = 9*A2 = 9*s2^2 --> s1^2 = 9s2^2
Taking the square root of both sides, we have:
s1 = 3*s2
Plugging s1 in to the equation for L, we get:
200 cm = 4(s1 + s2) = 4(3*s2 + s2) = 4*4*s2
s2 = 200 cm/16 = 12.5 cm
Thus s1 = 3*s2 = 37.5 cm
The perimeter P of the larger square is 4*s1, of
P = 150 cm
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