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.

Q: Answer-If the diagonal of a square is increased by 4 cm, its area increases by 56 cm2 . Find the ratio of t...

Area of Square A1 a2 ................... 1 Length of diagonal d1 2a .............. 2 From eq2 a d12 Area of square A1 d122 A1 d122 ........... 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 d222 From eq 3 we get, A2 d1 422 .......... 6 From eq 4 we get, A2 - A1 56 .......... 7 Substitute eq 3 and eq 6 in eq 7 d1 422 - d122 56 d1 42 - d12 56 2 d1 42 - d12 112 d12 8d1 16 - d12 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 d222 d122 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