Got it! You're describing a shape (likely a rectangle) where:
- The width is xx, the height is yy, and the diagonal is 5.5.
- This gives the equation:
x2+y2=5.52x2+y2=5.52
- When two of these shapes are placed side by side, the new width becomes 2x2x, the height stays yy, and the diagonal is 7.8.
- This gives the equation:
(2x)2+y2=7.82(2x)2+y2=7.82
Step 1: Write the Equations
Expanding the given equations:
x2+y2=30.25x2+y2=30.254x2+y2=60.844x2+y2=60.84
Step 2: Subtract the First Equation from the Second
(4x2+y2)−(x2+y2)=60.84−30.25(4x2+y2)−(x2+y2)=60.84−30.253x2=30.593x2=30.59x2=10.197x2=10.197x=10.197x=10.197x≈3.19x≈3.19
Step 3: Solve for yy
Substituting x2=10.197x2=10.197 into the first equation:
10.197+y2=30.2510.197+y2=30.25y2=30.25−10.197y2=30.25−10.197y2=20.053y2=20.053y=20.053y=20.053y≈4.48y≈4.48
Final Answer:
- Width x≈3.19x≈3.19
- Height y≈4.48y≈4.48
So, the original shape has dimensions
3.19×4.483.19×4.48, and when placed side by side, the combined shape is
6.38×4.486.38×4.48 with a diagonal of 7.8.
so maybe 3.2 inch x 4.48 inch that sound very pocketable