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.

Expert Answers
kjcdb8er eNotes educator| Certified Educator

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

ainsleyharris | Student