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what is the longest side of the rectangle?
A rectangle measures x+10 cm and x-10 cm, squares of side 3 cm are taken from each corner. The resulting shape has an area 264cm2. Find the length of the longest side of the rectangle
- JimLv 71 month ago
Total area = 264cm² + 2*(3cm x 3 cm) = 283 cm²
283 cm² = (x+10 cm) (x-10 cm) = x² -100
x = √383
x + 10 = 10 + √383 cm = 29.57 cm
- KrishnamurthyLv 71 month ago
A rectangle measures (x + 10) cm by (x - 10) cm.
Squares of side 3 cm are taken from each corner.
The resulting shape has an area of 264 cm^2.
(x + 4)(x - 16) = 264
x^2 - 12x - 328 = 0
x ≈ 25.079 cm
The length of the longest side of the rectangle is 25.079 cm.
- lenpol7Lv 71 month ago
A(rectangle) = ( x + 10)(x - 10) = x^2 - 100
The four corners are 4 x 3 x 3 = 36cm^2
x^2 - 100 - 36 = 264
x^2 = 136 + 264
x^2 = 400
x = +/-20
x = 20
Hence longest side is 20 + 10 = 30 cm
& shortest side is 20 - 10 = 10 cm