Final answer:
The perimeter of a rectangle, with a length to breadth ratio of 4:3 and a diagonal measuring 25 cm, is found using Pythagoras' Theorem. By solving for the common multiplier x, the dimensions are determined and the formula P = 2(length + breadth) yields a perimeter of 75 cm. The correct option is (B).
Step-by-step explanation:
The question asks us to find the perimeter of a rectangle with a known diagonal length and a ratio of length to breadth. The diagonal (25 cm) forms a right-angled triangle with the length and breadth. Since we are given the ratio of the length to breadth as 4:3, we can represent the length as 4x and the breadth as 3x, where x is a common multiplier.
Using Pythagoras' Theorem, we can write (4x)^2 + (3x)^2 = 25^2, which gives 16x^2 + 9x^2 = 625. Combining like terms, we get 25x^2 = 625, so x^2 = 25 and x = 5. Therefore, the length is 4x = 20 cm and the breadth is 3x = 15 cm.
The formula for the perimeter (P) of a rectangle is P = 2(length + breadth), so P = 2(20 cm + 15 cm) = 2(35 cm) = 70 cm. Therefore, the correct option for the perimeter of the rectangle is Option B. 75 cm.