Video Transcript
A rhombus and a square have the
same area. If the square’s perimeter is 44 and
one of the diagonals of the rhombus is 10, how long is the other diagonal to two
decimal places?
So we have a rhombus and a square
which have the same area. And we’re given some other
information about each shape. First, the perimeter of the square
is 44 units. And secondly, one of the diagonals
of the rhombus is of length 10 units. As we’re told that the areas of
these two shapes are the same, this must be key information. So let’s begin by calculating the
area of a square. We know that the area of a square
is its side length squared. As we know that the perimeter of
this square is 44 units, we know that four times the side length is equal to 44. And then dividing both sides of
this equation by four, we find that the side length of the square is 11 units. So its area is 11 squared, which is
121 square units.
We now know that the area of both
the square and the rhombus is 121 square units. And we want to use this information
in conjunction with the fact that one diagonal of the rhombus is of length 10 units
to calculate the length of the other diagonal. We should recall that the area of a
rhombus is half the product of the lengths of its diagonals, 𝑑 one 𝑑 two over
two. So, as we already know the length
of one diagonal is 10 units and the area is 121 square units, we have that 10
multiplied by the length of the second diagonal over two is equal to 121. Simplifying, we find that five
multiplied by the length of the second diagonal is 121. And then dividing both sides of
this equation by five, we find that the length of the second diagonal is 121 over
five or 24.2 units. We were asked to give the answer to
two decimal places though, so that’s 24.20 units.
