the length of a rectangle is 1 meter less than its width. the area of the rectangle is 42 square meters. find the dimensions of the rectangle.

A) L = W -1
B) L * W = 42
B) L = 42 / W
substituting this into A
A) 42 / W = W -1
Multiplying both sides by "W"
A) 42 = W^2 -W
A) W^2 -W - 42 = 0
W = 7
Length = 6

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JeanaShupp JeanaShupp · Answer 2 · 2019-03-19T10:52:13+01:00

Answer: Width of rectangle = 7 meters

Length of rectangle 7-1=6 meters

Step-by-step explanation:

Let w (meters) be the width of the rectangle, then (w-1) (meters ) will be its length.

Now, we know that the area of rectangle is given by :-

[tex]\text{Area}=length\times width[/tex]

Therefore, for the given rectangle , the area of rectangle will be

[tex]w(w-1)=42\\\\\Rightarrow w^2-w=42\\\\\Rightarrow w^2-w-42=0\\\\\Rightarrow w^2+6w-7w-42=0\\\\\Rightarrow (w+6)(w-7)=42\\\\\Rightarrow w=7 or w=-6 \\\\\Rightarrow w=7....[\text{w cannot be negative}][/tex]

Hence, the width of rectangle = 7 meters

Length of rectangle 7-1=6 meters