Square side

Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.

Result

a =  1.77

Solution:

v(A,BD)=∣−4⋅0+⋅0−5∣(−4)2+02=1.25 u=∣AC∣=∣BD∣=2⋅v(A,BD)=2.5  u=2a a=u/2=1.77v(A, BD) = \dfrac{|-4\cdot 0+\cdot 0 -5|}{\sqrt{ (-4)^2 + 0^2}} = 1.25 \ \\ u = |AC| = |BD| = 2 \cdot v(A, BD) = 2.5 \ \\ \ \\ u = \sqrt2 a \ \\ a = u / \sqrt2 = 1.77

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Following knowledge from mathematics are needed to solve this word math problem:

For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc. Pythagorean theorem is the base for the right triangle calculator.

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