OG详解-OG4 数学1 Q17

Choice B is correct. It’s given that the ratio of the rectangular region’s length to its width is 35 to 10. This can be written as a proportion: lengthwidth​​ ​= 3510​​ , or  lw​​= 3510​​. This proportion can be rewritten as 10ℓ= 35w, or ℓ= 3.5w. If the width of the rectangular region increases by 7, then the length will increase by some number x in order to maintain this ratio. The value of x can be found by replacing ℓ with ℓ+ x and w with w + 7 in the equation, which gives ℓ+ x = 3.5(w + 7). This equation can be rewritten using the distributive property as ℓ+ x = 3.5w +24.5. Since ℓ= 3.5w, the right-hand side of this equation can be rewritten by substituting ℓ for 3.5w, which gives ℓ+ x = ℓ+24.5, or x = 24.5. Therefore, if the width of the rectangular region increases by 7 units, the length must increase by 24.5 units in order to maintain the given ratio.
Choice A is incorrect. If the width of the rectangular region increases, the length must also increase, not decrease. Choice C is incorrect. If the width of the rectangular region increases, the length must also increase, not decrease.Choice D is incorrect. Since the ratio of the length to the width of the rectangular region is 35 to 10, if the width of the rectangular region increases by 7 units, the length would have to increase by a proportional amount, which would have to be greater than 7 units.