Question

the sum of the perimeters of two squares is 50cm and the sum of the areas is 93.25cm^2. find the side length of each square.

Answer 1

Answer:

S₁ = 9 cm. S₂ = 3.5 cm.

Step-by-step explanation:

Let S₁ and S₂ be the sides of the two squares.

Sum of the perimeters = 50

4S₁ + 4S₂ = 50

=> S₁ + S₂ = 25/2.  ----------------- [1]

Sum of Areas = 93.25

S₁² + S₂² = 93.25

(S₁ + S₂)² = S₁² + S₂² + 2S₁S₂

(12.5)² = 93.25 + 2S₁S₂

2S₁S₂ = 156.25 - 93.25 = 63

S₁S₂ = 63/2.

S₁ - S₂ = √ (S₁ + S₂) ² - 4S₁S₂

           = √(25/2)² - 4*63/2

            = √625/4 - 126 = √121/4 = 11/2.  ---------------- [2]

Solve [1] and [2] by adding

S₁ + S₂ = 25/2

S₁ - S₂ = 11/2

-----------------------

2S₁ = 36/2

=> S₁ = 9 cm.

Substitute value of S₁ in [1],

9 + S₂ = 25/2

=> S₂ = 25/2 - 9  = 7/2 = 3.5 cm.

              = (25/2)