Start learning 50% faster. Sign in now
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
If A: B = 2:3 and B: C = 3:4 find the value of (A+B): (B+C): (C+A).
₹ 6,900 is divided between L, M and N in the ratio of 6: 8: 9. If 'L' and 'M' each gave ₹ 300 to N then the new ratio of shares of L, M and N is:
The speed of the boat A and B in still water are in the ratio 15:13. The speed of the current for both boats is 16 km/hr. If the sum of time taken by bo...
If a student distributes sweets in the ratio of 1/2:1/3:1/4:1/5:1/6 among five of his friends A, B, C, D and E, then the total number (minimum) of swe...
In a college the ratio of boys and girls are in the ratio 7:9. 65% girls and 40% boys were absent. Find the girls present if the total number of student...
The ratio between the length and breadth of a rectangular board is 7:5. If the breadth of the board is 20.5cm, find the length in cm.
In a town, the ratio of males to females is 5:4. Among the males, 20% are children, and the rest are adults. If the adult male population is 4,500, what...
A is thrice as efficient as B and C is twice as efficient as B. What is the ratio of number of days taken by A, B and C when they work individually?
The ratio of three numbers is 3 : 5 : 4 and the sum of their squares is 11250. Find the sum of the numbers .
Two boxes have chocolates in the ratio 7:5. If the difference in the number of chocolates is 28, find the number of chocolates in the box with larger nu...