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If the area of a square A has area 24 cm2, then what is the area of another square B having diagonal two-third of the diagonal of A?1). 26 cm22). 42.5cm23). 32/3 cm24). 38.6 cm2 |
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Answer» Given: Area of square A = 24 sq.cm To find : Area of square B = ? Let us take the side of square A as 'a' and square B as 'b'. So, a²= 24 sq.cm a = √24 a = 2√6 cm. It is given that, Diagonal of square B = two-third of the diagonal of square A We KNOW that diagonal of a square = √2 of side of a square So, √2 (b) = (⅔)√2 (a) b = (⅔) a SUBSTITUTING the value of a in here we have b = ⅔ ( 2√6 ) b = ( 2 × 2√2 √3 ) / (√3 √3) b = (4 √2)/√3 cm Area of square B = b² cm² Area of square B =[(4 √2)/√3]² cm² Area of square B = (16×2) / 3 cm² Area of square B = 32/3 cm² So,the correct option is 3). 32/3 cm² |
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