Brendan has a rectangular paved area in his backyard. If the length and breadth were increased by the same percentage and the area increases by 21%, what is the percentage increase of the length and breadth?
1.21 L W = x L * x W
1.21 = x^2 ... x = 1.1 ... a 10% increase
To find the percentage increase of the length and breadth, we need to first understand the relationship between the area of a rectangle and its length and breadth.
The area of a rectangle is given by the formula: Area = Length × Breadth.
Let's say the initial length of Brendan's rectangular paved area is L and the initial breadth is B. The initial area can be expressed as: Initial Area = L × B.
Now, if the length and breadth are increased by the same percentage, let's say x%, the new length would be (100 + x)% of the initial length, and the new breadth would also be (100 + x)% of the initial breadth.
So, the new length would be L × (1 + x/100), and the new breadth would be B × (1 + x/100).
The new area can be calculated by multiplying the new length and new breadth: New Area = L × (1 + x/100) × B × (1 + x/100).
We are given that the new area is 21% greater than the initial area.
So, we can write the equation: New Area = Initial Area + 21% of Initial Area.
Substituting the values, we get: L × (1 + x/100) × B × (1 + x/100) = Initial Area + 0.21 × Initial Area.
Simplifying further, we get: (1 + x/100)² = 1 + 0.21.
Taking the square root of both sides and solving for x, we can find the percentage increase of the length and breadth.
However, to calculate the value of x precisely, we need the specific values of the initial length and breadth or the ratio between them.
Once those values are provided, we can substitute them into the equation to solve for x, which would give us the percentage increase of the length and breadth.