Answer:
the length of its diagonal is √2
Step-by-step explanation:
Data provided:
The square is drawn on one side of the right triangle
also,
Length of each side of square is 1 units
Now, let the length of the diagonal be 'X'
also,
The diagonal of the square will be the hypotenuse of the right triangle
we know the property of the right triangle that
Base² + Perpendicular² = Hypotenuse²
OR
1² + 1² = X²
or
X² = 2
or
X = √2
Hence,
the length of its diagonal is √2
Answer:
Step-by-step explanation:
In the image attached, you can observe that one leg of the right triangle has the same length than a side of the square below, that means we need to find that leg length.
Using Pytagorean's Theorem, we have
[tex]6^{2}=4^{2}+l^{2} \\36-16=l^{2}\\ l=\sqrt{20}=2\sqrt{5}[/tex]
Therefore, each side of the square as a lenght of [tex]2\sqrt{5}[/tex] units.
Now, notice that the right triangle inside the square has its hypothesus congruent with the diagonal, using the lengt of each side of the square, we can find the diagonal length.
[tex]d^{2}=(2\sqrt{5})^{2} +(2\sqrt{5})^{2} =4(5)+4(5)=20+20=40\\d=\sqrt{40}\\ d=2\sqrt{10}[/tex]
Therefore, the diagonal length is [tex]2\sqrt{10}[/tex] units.
