The side of a square exc.eeds the side of the another square by 4cm and the sum of the area of two squares is 400 sq.cm. Find the sides of two squares.
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Answer:
The sides of two squares are 16 cm and 12 cm
Step-by-step explanation:
Given,
- The side of a square exceeds the side of the another square by 4cm
- the sum of the area of two squares is 400 sq.cm
To find,
- the sides of two squares
Solution,
Let
- side of the square 1 be 'a' cm
- side of the square 2 be 'b' cm
The side of a square exceeds the side of the another square by 4cm
➙ a = b + 4
we know,
Area of the square = (side)²
Area of square 1 = a²
Area of square 2 = b²
the sum of the area of two squares is 400
➙ a² + b² = 400
➙ (b + 4)² + b² = 400
➙ b² + 4² + 2(b)(4) + b² = 400
➙ 2b² + 16 + 8b = 400
➙ 2b² + 8b + 16 - 400 = 0
➙ 2b² + 8b - 384 = 0
➙ 2(b² + 4b - 192) = 0
➙ b² + 4b - 192 = 0
➙ b² + 16b - 12b - 192 = 0
➙ b(b + 16) - 12(b + 16) = 0
➙ (b + 16) (b - 12) = 0
➙ b = -16 , 12
The dimension can not be negative.
Therefore, side of the square 2, b = 12 cm
⇒ a = b + 4
a = 12 + 4
a = 16 cm
The sides of two squares are 16 cm and 12 cm
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