Question
If the diagonal of a square is increased by 4 cm, its
area increases by 56 cm2 . Find the ratio of the new area of the square to the initial area of the square.Solution
Area of Square (A1) = a2 ................... (1) Length of diagonal (d1) = √2a .............. (2) From eq(2) → a = d1/√2 Area of square (A1) = (d1/√2)2 A1 = (d1)2/2 ........... (3) ∴ Diagonal of square increased by 4cm and its are increases by 56cm2. Increased diagonal of square (d2) = d1 + 4 ........... (4) Increased area of square (A2) = A1 + 56 .......... (5) A2 = (d2)2/2 From eq (3) we get, A2 = (d1 + 4)2/2 .......... (6) From eq (4) we get, A2 - A1 = 56 .......... (7) Substitute eq (3) and eq (6) in eq (7) ⇒ (d1 + 4)2/2 - (d1)2/2 = 56 ⇒ (d1 + 4)2 - (d1)2 = 56 × 2 ⇒ (d1 + 4)2 - (d1)2 = 112 ⇒ (d1)2 + 8d1 + 16 - (d1)2 = 112 ⇒ 8d1 + 16 = 112 ⇒ 8d1 = 112 - 16 ⇒ 8d1 = 96 ⇒ d1 = 12 ∴ d2 = d1 + 4 d2 = 12 + 4 = 16 Ratio of the new area of the square to the initial area of the square = A2 / A1 A2 / A1 = ((d2)2/2) / ((d1)2/2 ) A2 / A1 = (162 / 2) / (122 / 2) A2 / A1 = (256 / 2) / (144 / 2) A2 / A1 = 128 / 72 A2 / A1 = 16 / 9 ∴ Here, Ratio of the new area of the square to the initial area of the square A2 : A1 = 16 : 9
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)
22.22 × 8.99 + 142.15 = ?
(10.013 – 12.04) = ? + 7.98% of 4999.98
960.11 ÷ 23.98 × 5.14 – 177.9 = √?
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)
90.004% of 9500 + 362 = ?
(4096)1/3 × 10.11 × 11.97 ÷ 24.32 = ? + 15.022
20.22% of (61.9 × 5.01) + 69.97 =?
The base of a prism is an equilateral triangle with a perimeter of 36 cm. If the height of the prism is 12 cm, calculate the volu...
(1560.23 ÷ 25.98) + (768.32 ÷ 23.9) + 1814.11 = ?
Relevant for Exams:
