Find the original dimensions
If the smaller dimension of a rectangle is increased by
meters and the larger dimension by
meters, one dimension becomes
of the other, and the area is increased by
square meter. Find the original dimensions of the rectangle.
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1 solution
Carefully reading the problem, let x be the original smaller dimension and y be the original larger dimension. It follow these two equations:
5 3 = y + 5 x + 3 ⇒ 3 y + 1 5 = 5 x + 1 5 ⇒ 3 y = 5 x
( x + 3 ) ( y + 5 ) − x y = 1 3 5 ⇒ x y + 5 x + 3 y + 1 5 − x y = 1 3 5 ⇒ 5 x + 3 y = 1 2 0
Using a substitution with 3 y = 5 x into the second equation, we get to:
5 x + 3 y = 1 2 0 ⇒ 5 x + 5 x = 1 2 0 ⇒ x = 1 2
going back to equation 1, using x=12, we get:
3 y = 5 x ⇒ 3 y = 5 ⋅ 1 2 ⇒ y = 2 0
All of this was done with meters being the understood units. :)