The number of inches by which each dimension must be increased is 10 inches.
Let length and width be increased by x.
so we get, the length = (10 + x) and breadth = (5 + x)
(10 + x)(5 + x) = 6 × 10 × 5
50 + 10 x + 5x + x² = 300
x² + 15x- 250 = 0
x² + 25x- 10x - 250 = 0
x (x + 25) - 10 (x + 25) = 0
(x + 25)(x - 10) = 0
x = -25 is not the right choice as length cannot be negative.
so x = 10
so both dimensions should be increased by 10 inches.
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The complete question is -
A rectangular picture frame is 5 inches wide and 10 inches tall. You want to make the area 6 times as large by increasing the length and width by the same amount. Find the number of inches by which each dimension must be increased.
