Question

If the area of the larger square is subtracted from twice the area of the smaller square, then the result is 8 cm^2. However, if 3 times the area of the smaller square is added to 2 times the area of the larger square, then the result is 236 cm^2. Determine the side of the two squares.

Answer 1

Let the area of larger square be a and area of smaller square be b, then

a - 2b = 8 ..

a = 8 + 2b..........(equation 1)

3b + 2a = 236..

Now using the value of a from equation 1 we get

3b + 2(8 + 2b)= 236

3b + 16 + 4b = 236

7b + 16 = 236

7b = 236 - 16

7b = 220

b = 220/ 7

b = 31.5 ( approximate)

Now to find the value of a we will use the value of b:

a - 2b = 8

a - 2 ( 31.5)= 8

a - 63 = 8

a= 8 + 63 = 71

side of smaller square :

area = 4 × side

31.5 /4 = side

side = 7.8 cm

side of larger square :

area = 4 × side

71 /4= side

side = 17.8cm

Hence the sides of squares are:

smaller square= 7.8cm

larger square = 17.8cm

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