Respuesta :
Answer:
16 meters by 26 meters.
Step-by-step explanation:
Let x represent the width of the road.
Please consider the complete question.
A rectangular tract of land 20 m x 30 m has part of its area covered by an L-shaped road, which goes around two sides. The road is the same width on both sides, and its area is 184 m². What are the dimensions of the part of the tract of land not covered by the road?
First of all, we will find the area of the rectangular tract by multiplying its dimensions as:
[tex]\text{Area of tract}=20\text{ m}\times 30\text{ m}[/tex]
[tex]\text{Area of tract}=600\text{ m}^2[/tex]
Area of the tract of land not covered by the road would be total area minus area of the road.
[tex]\text{Area of the tract of land not covered by the road}=600\text{ m}^2-184\text{ m}^2[/tex]
[tex]\text{Area of the tract of land not covered by the road}=416\text{ m}^2[/tex]
The dimension of the tract without road would be dimensions of tract minus width of the road that is [tex](20-x)[/tex] and [tex](30-x)[/tex].
The expression for the area of tract without road would be:
[tex](20-x)(30-x)[/tex]
[tex](20-x)(30-x)=416[/tex]
Let us solve for x.
[tex]600-20x-30x+x^2=416[/tex]
[tex]x^2-50x+600=416\\\\x^2-50x+184=0[/tex]
[tex]x^2-46x-4x+184=0[/tex]
[tex]x(x-46)-4(x-46)=0\\\\(x-46)(x-4)=0\\\\x=46\text{ or }x=4[/tex]
Since width of 46 meter is not possible, so width of the road would be 4 meters.
Dimensions of the track not covered by the road would be [tex](20-x)\Rightarrow 20-4=16[/tex] and [tex](30-x)\Rightarrow 30-4=26[/tex].
Therefore, the dimensions of the part of the track not covered by the road would be 16 meters by 26 meters.
