Q). Sum of the areas of two squares is 157 m². If the sum of their perimeters is 68 m, find the sides of the two squares.

Ans:

Let’s consider that the side of a square is X m and the side of the other square is Y m.

Step 1: By 1st given condition, A₁ + A₂ = 157

∴ X² + Y² = 157 ……….. (i)

Step 2: By 2nd given condition, P₁ + P₂ = 68

∴ 4 X + 4 Y = 68

∴ X + Y = 17 ………….(ii)

∴ X = 17 – Y ………….(iii)

Step 3: By substituting value of X from equation (iii) in equation (i), we get:

X² + Y² = 157

∴ (17 – Y)² +Y² = 157

∴ 289 + Y² – 34 Y + Y² = 157

∴ 2 Y² – 34 Y + 289 – 157 = 0

∴ 2 Y² – 34 Y + 132 = 0

∴ Y² – 17 Y + 66 = 0

Step 4: We solve the above quadratic equation by mid term splitting:

∴ Y² – 11 Y – 6 Y + 66 = 0

∴ Y (Y – 11) – 6 (Y + 11) = 0

∴ (Y – 6) (Y – 11) = 0

∴ Y = 6 and Y = 11

Step 5: By substituting value of Y in equation (i), we get:

X = 17 – Y

∴ at Y = 6, X = 17 – 6 = 11

and at Y = 11, X = 17 – 11 = 6

Here, we get X = 11 at Y = 6 and X = 6 at Y = 11

Therefore, the sides of one square is 6 m and the side of the other square is 11 m.

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