Question

The diagram shows a sequence of square wire frames. The lengths of a side of these frames
are x cm, (x+ 3) cm, (x+6) cm......respectively. The sum of the areas of the first three
squares is 525 sq cm.
1. Express the length of a side of the frame Square wire frames
in terms of x and n
2. Find the value of x
3. piece of wire is 99 cm long. It is cut and
bent into a frame in the sequence Find the length of a side of the largest frame than can be formed.

Answer 1

Length of wire frames and side of frame -

• Side of first three wire frames = x. x+3, x+6
• Areas of wire frames = x², x+3², x+6²
• Sum of areas of wire frames = 525cm²
• Therefore, x²+ x²+9+6x + x²+36+12x = 525
• 3x²+  45+ 18x= 525
• 3x²+18x-480

• roots  = x² +16x-10x -160 =0
• x(x+16) -10(x+16) =0
• x= 10
• Length of side of frame in terms of x and n = x + 3n, where n = 0,1,2,3.....
• If wire ==99cm, perimeter of square after bending = 99cm
• therefore, 4s = 99, where s = side of square
• Side = 99/4 = 24.75cm

Answer 2

Answer:

1. x+3n-3

2. x=10

3. 24.75 cm