AI Math Solver
Resources
Questions
Pricing
Login
Register
Home
>
Questions
>
Solve for x and Find Square Diagonal Length with Given Half-Diagonal Segments
Mathematics
Grade 8 (Junior High School)
Question Content
In square WZYX with diagonals intersecting at R, WR = 5x - 13 and ZR = 3x + 11. Solve for x and find the length of ZX.
Correct Answer
x = 12, ZX = 74
Detailed Solution Steps
1
Step 1: The diagonals of a square bisect each other, so WR = ZR.
2
Step 2: Set up the equation: \(5x - 13 = 3x + 11\).
3
Step 3: Solve for x: Subtract 3x from both sides: \(2x - 13 = 11\). Add 13 to both sides: \(2x = 24\). Divide by 2: \(x = 12\).
4
Step 4: Calculate ZR by substituting x=12: \(ZR = 3(12) + 11 = 36 + 11 = 47\).
5
Step 5: ZX is a diagonal, which is twice ZR: \(ZX = 2×47 = 74\).
Knowledge Points Involved
1
Bisecting Diagonals of a Square
The diagonals of a square intersect at their midpoints, so the segments from the intersection to each vertex are equal in length.
2
Solving Linear Equations with Variables on Both Sides
For equations with variables on both sides, first collect like terms by subtracting the smaller variable term from both sides, then isolate the variable using inverse operations.
3
Square Diagonal Length from Half-Segment
The full length of a square's diagonal is twice the length of the segment from the intersection point to a vertex.
Loading solution...
