Video Transcript
The length of a rectangular piece
of land is one meter longer than two times the width. The perimeter is 150 meters. Find the dimensions of this
rectangular piece of land.
In this question, we are asked to
find the dimensions of a rectangular piece of land. To do this, we are told that the
perimeter of the land is 150 meters and that the length of the rectangle is one
meter longer than two times the width.
To answer this question, let’s
start by sketching the rectangular piece of land. We can say that it has a length of
𝑙 meters and a width of 𝑤 meters. We are told in the question that
the length of the rectangle is one meter longer than twice the width. This means that if we double the
width and add one meter, we will have an expression equal to the length of the
land. Therefore, 𝑙 is equal to two 𝑤
plus one.
We can also recall that the
perimeter of a polygon is the sum of its side lengths. So the perimeter of a rectangle is
twice its length plus twice its width. Since we are told that the
perimeter is 150 meters, we must have 150 equals two 𝑙 plus two 𝑤. We can construct an equation
involving only 𝑤 by substituting the expression for 𝑙 into the perimeter
equation. Substituting 𝑙 equals two 𝑤 plus
one into the equation gives us 150 is equal to two times two 𝑤 plus one plus two
𝑤.
We now have an equation in terms of
𝑤 that we want to solve for 𝑤. To do this, we need to isolate 𝑤
on one side of the equation. We can start by distributing the
factor of two over the parentheses. Doubling each term inside the
parentheses gives us that 150 is equal to four 𝑤 plus two plus two 𝑤. We can simplify the right-hand side
of the equation by collecting the like terms. We have four 𝑤 plus two 𝑤 equals
six 𝑤. We can now solve for 𝑤 by
isolating 𝑤 on the right-hand side of the equation. We subtract two from both sides of
the equation. This gives us 148 is equal to six
𝑤.
We can then divide both sides of
the equation by six to obtain that 𝑤 is equal to 148 over six. We can simplify this fraction by
dividing both the numerator and denominator by two. This gives us that the width of the
rectangular piece of land is 74 over three meters. We can find the length of the land
by recalling that it is twice the width plus one meter. Substituting 𝑤 equals 74 over
three into the equation and calculating gives us that 𝑙 is equal to 151 over
three.
Hence, the width of the rectangular
piece of land is 74 over three meters, and the length is 151 over three meters.
