Question

If two sides of a square lies on the lines 5x-12y+26=0 and 5x-12y-65=0, find its area.

Answer 1

Hope u know the formula of distance between two parallel lines

Answer 2

Area of square is 49 square units.

Step-by-step explanation:

Given:

Here two sides of a square lies on the lines 5x-12y+26=0 and 5x-12y-65=0.

So,  5x-12y=-26, 5x-12y=65

Both lines are parallel because slope are same.

Then obviously distance between both line would be the side of square.

If there are two lines Ax1 + By1 = C1 and Ax2 + By2 = C2.

Then distance = $\frac{| C1 - C2 |}{\sqrt{A^2+B^2} }$

Distance = $\frac{|-26-65|}{\sqrt{5^2+12^2}}$

                = $\frac{|-91|}{\sqrt{25+144} }$

               = $\frac{|91|}{13}$

Distance = 7    

Area of square = $side^2$

                          = $7^2$

                          = 49 square units.