Question

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.

Answer 1

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

Answer 2

Answer: Width of rectangle = 7 meters

Length of rectangle 7-1=6 meters

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 :-

`\text{Area}=length* width`

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

`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}]`

Hence, the width of rectangle = 7 meters

Length of rectangle 7-1=6 meters