Question #c477a

1 Answer
EZ as pi
Mar 16, 2017

The new width #= 16 # metres and new length #= 24# metres

Explanation:

There are two different rectangles to consider. Once we have have chosen a variable, we can write an expression for each side of the rectangles in term of that variable.

Let the width of the smaller garden be #x#
The length is #4m# longer, which gives #x+4#

The shorter perimeter will be #2 (x+x+4) = 4x+8#

For the larger garden, the width is #x+8#
and the length is #x+4 +12 = x+16#

The longer perimeter will be #2(x+8+x+16) = 4x +48#

The bigger perimeter is twice as big as the smaller:

[#2# times smaller = bigger]

#2(4x+8) = 4x+48" "div 2#

#4x+8 = 2x +24#

#2x = 16#

#x =8#

The old garden has width =#8# and length = #12#

The new garden has width #= 16#metres

and length #= 24# metres

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