Question

Sum of the areas of two squares is 400 cm . If the difference of their perimeters is 16 cm, find the sides of the two squares.
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Answer 1

➝ Correct question :-

Sum of the areas of two squares is 400 cm². If the difference of their perimeters is 16 cm, find the sides of the two squares.

➝ Given :-

⇾sum of the area of 2 squares is 400cm²

difference of their perimeters is 16cm

➝ To find :-

⇾the sides of the 2 squares

➝ Solution :-

Let the sides of the given squares be a cm and b cm respectively. Then,

→ a² + b² = 400. ....(i)

→ 4a - 4b = 16

→ a - b = 4. .....(ii)

Squaring (ii) on both sides, we get

⟹ (a - b)² = 16 = (a² +b²) – 2ab = 16

⟹ 400 - 2ab = 16 [using (i)]

⟹ 2ab = 384 = ab = 192. .....(iii)

now, (a+b)² – (a –b)² = 4ab

⟹ (a + b)² –16 = 4 x 192.

⟹ (a + b)² = 768 + 16 = 784

⟹ a + b = √768 = 28.

On solving a +b = 28 and a - b = 4

→ a = 16

→ b = 12

Hence, the sides of the given squares are 16 cm and 12 cm.