Final answer:
To find the length of the diagonal of a rectangle where the breadth is 3m less than its length and the perimeter is 26m, you first calculate the length as 8m and the breadth as 5m. Then, using the Pythagorean theorem, the diagonal approximately measures 9.434 meters.
Step-by-step explanation:
Finding the Length of a Rectangle's Diagonal
Let's denote the length of the rectangle by L and the breadth by B. According to the problem, the breadth is 3 meters less than the length, which gives us the relationship B = L - 3m. The perimeter of the rectangle is given as 26 meters, which can be expressed with the formula P = 2L + 2B. Thus, we have 26m = 2L + 2(L - 3m).
Now, let's find L step by step:
- 26m = 2L + 2L - 6m
- 26m + 6m = 4L
- 32m = 4L
- L = 8m
Therefore, the length (L) of the rectangle is 8 meters, and the breadth (B) would be L - 3m = 8m - 3m = 5m.
Now, to find the length of the diagonal, we use the Pythagorean theorem because the diagonal of a rectangle forms a right triangle with the length and breadth. The length of the diagonal (d) can be calculated by d = \(√(L^2 + B^2)\). Plugging in the values of L = 8m and B = 5m, we get:
- d = \(√(8m)^2 + (5m)^2\)
- d = \(√64m^2 + 25m^2\)
- d = \(√89m^2\)
- d ≈ 9.434 meters
Thus, the length of the diagonal of the rectangle is approximately 9.434 meters.