Question

Two sides of the square are on the line x + 7y - 2 = 0 and x + 7y - 10 = 0. Find the area of the square.

2. What is the area of the circle circumscribing a triangle bounded by the lines 2x + y – 10 = 0, x + 5 = 0, and y + 4 = 0?
Please include your complete solution so I can learn from it.

Answer 1

To find the area of the square, solve for the intersection point of two lines and calculate the distance between them. The length of one side of the square is 6 units, so the area of the square is 36 square units.

Step-by-step explanation:

To find the area of the square, we first need to find the length of its sides. The given lines x + 7y - 2 = 0 and x + 7y - 10 = 0 represent two sides of the square. We can find the intersection point of these lines by solving the two equations.

Solving these equations, we get x = -8 and y = 1. Now we can find the distance between these two points which will give us the length of one side of the square.

Using the distance formula, we get sqrt((-8 - (-2))^2 + (1 - 1)^2) = 6.

Since a square has equal sides, the length of all four sides of the square is 6. Now we can find the area of the square by squaring the length of one side.

So the area of the square is 6^2 = 36 square units.