If the digonal of a rectangle is square root of 89. Find the lenght and breadth ?
Please want the ans
there are many such rectangles.
1 x √88
2 x √85
...
√44 x √45
To find the length and breadth of a rectangle when given the diagonal, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the other two sides (length and breadth in this case).
Let's denote the length as 'l' and the breadth as 'b'. So we have:
l² + b² = diagonal²
In this case, the diagonal is the square root of 89. Therefore, the equation becomes:
l² + b² = √89²
l² + b² = 89
Since we have two variables and only one equation, we cannot find the length and breadth uniquely. However, we can solve for them in terms of each other by assuming a value for one of them.
For example, let's assume the length (l) is equal to 7. We can then substitute this value into the equation and solve for the breadth (b):
7² + b² = 89
49 + b² = 89
b² = 89 - 49
b² = 40
b = √40
b = 2√10
So, with the length assumed as 7, the breadth would be 2√10.
Remember that this is just one possible solution assuming a value for either length or breadth. You could also assume a different value for length and solve for breadth using the same process.