Video Transcript
Two plots of land have the same
area. One is a square, and the other is a
rhombus with diagonals of lengths 48 meters and 35 meters. What is the perimeter of the square
plot? Give your answer to two decimal
places.
In this question, it might be
helpful to draw some diagrams to visualize the problem. We’re told that there’s two plots
of land, and one is a square, and the other is a rhombus. Let’s draw the square. We know that this will be a
quadrilateral with four sides of the same length and all the interior angles will be
90 degrees. When it comes to the rhombus, we
know that this will be a quadrilateral with all four sides the same length. On this diagram, we can put the
double markation on the lines so that we don’t get confused into thinking the
lengths of this rhombus will be the same as the lengths of the square.
The other information that we’re
given is the lengths of the diagonals on the rhombus. The longer one is 48 meters, and
the shorter one is 35 meters. We’re also told that these two
plots of land, the square and the rhombus, have the same area. And we’re asked to find the
perimeter of the square plot. We can remember that the perimeter
of a shape is the distance around the outside. We could do this if we had the
length of the side of the square, but we don’t; we’ll need to calculate it. Let’s see if we can find the area
of the rhombus. To do this, we’ll need to recall a
certain formula.
We can find the area of a rhombus
using the two diagonals 𝑑 sub one and 𝑑 sub two by multiplying 𝑑 sub one and 𝑑
sub two and then dividing by two. We can simply plug in our two
diagonals of 35 and 48 to work out 35 times 48 over two. It’s always good to simplify a
calculation when we can. We’re asked to give our answer to
two decimal places here, so we can assume that a calculator would be allowed.
Either by using a calculator or by
a written method, we’ll get our answer of 840. And as it’s an area, our units will
be square meters. We were told that the areas were
the same, which means that the square will also have an area of 840 square
meters. We’ll need to remember that the
area of a square is equal to the length squared. And this time, we’re plugging in
the fact that the area is 840. So, we have 840 is equal to 𝐿
squared. In order to find the value of 𝐿,
we would take the square root of both sides of our equation. So, 𝐿 is equal to the square root
of 840. As we’re dealing with a length, the
units will be in meters.
It’s always tempting to pick up our
calculator and find the decimal value for this. But as we still need to find the
perimeter, we’ll keep our answer in the square root form. We remember that the perimeter of
the square will be the distance around the outside edge, which means that we’ll be
working out four multiplied by the square root of 840. Using our calculator, we get the
decimal value of 115.93101 and so on meters. Rounding to two decimal places
means we check our third decimal digit to see if it’s five or more. And as it isn’t, then our answer
rounds down to give us the perimeter of the square is 115.93 meters.
