Video Transcript
Find the diagonal length of a
square whose area equals that of a rectangle having dimensions of 10 centimeters and
35 centimeters.
The best place to begin here is by
modeling our two shapes, the square and the rectangle. The rectangle has a length and a
width of 10 centimeters and 35 centimeters. And we need to find the diagonal
length of the square. The information that we’re given to
allow us to work out the diagonal length is that the area of our two quadrilaterals
is the same. We don’t have any length
information about the square, so let’s see if we can work out the area of this
rectangle.
We can recall that the area of a
rectangle is equal to the length multiplied by the width. We would then fill in our two
values of 35 and 10, and working out 35 multiplied by 10 is nice and simple, 350
square centimeters. And so the area of our square will
also be 350 square centimeters. We’ll need to remember a formula
that connects the area of a square with its diagonal. The area of a square is equal to
the diagonal 𝑑 squared over two. As we want to find the diagonal
given the area, then we can use the rearranged form of this formula to give us that
𝑑 is equal to the square root of two 𝐴, where 𝐴 is the area of the square.
We can fill in the value for the
area that we know, keeping the letter 𝑑 as that’s the unknown that we want to find
out. 𝑑 is equal to the square root of
two multiplied by 350, which simplifies to 𝑑 is equal to the square root of
700. Assuming we’re using a
non-calculator method, we’ll need to simplify this square root further. We should hopefully notice this
nice square factor of 100. And therefore, we can break down
our calculation into the square root of 100 multiplied by the square root of seven,
which simplifies to 𝑑 equals 10 root seven. As 𝑑 is the diagonal length, then
we can give our final answer of 10 root seven centimeters.
