the area of a square garden in square feet is 49x^%2-14x+1. Find the dimensions of the garden in terms of x.
Factor 49x2 -14x + 1, it should be a perfect square.
To find the dimensions of the square garden, we need to factor the expression 49x^2 - 14x + 1 and identify the perfect square.
Let's factor the expression:
49x^2 - 14x + 1
This is a quadratic trinomial, which can be factored into two binomials in the form: (px + q)^2, where p and q are constants.
To find the values of p and q, we need to look for the perfect square trinomial pattern. The pattern is:
(a + b)^2 = a^2 + 2ab + b^2
Comparing this pattern to our expression, we can see that a^2 = 49x^2, which means a = 7x. Similarly, b^2 = 1, which means b = 1.
Using the perfect square trinomial pattern, we can rewrite the expression:
(7x + 1)^2
Therefore, the expression 49x^2 - 14x + 1 is a perfect square and can be factored as (7x + 1)^2.
Now that we have factored the expression, we can determine the dimensions of the square garden.
In a square garden, the length and width are equal, so both dimensions can be represented by (7x + 1). So, the dimensions of the garden in terms of x are (7x + 1) by (7x + 1).