Answer
Verified
396.9k+ views
Hint:As we know the side of the given square is \[10cm\]. And in a square, all the four sides are equal to each other as well as all the sides interest to its adjacent side at \[{90^0}\]. Therefore, the figure formed by joining the two opposite vertices of a square, is a right-angled triangle with two equal sides.
Complete step-by- step solution:
Given that Side of the square is \[10cm\]
In right angled\[\vartriangle ABC\]
Using Pythagoras theorem
\[A{B^2} + B{C^2} = A{C^2}\] \[\left[ {Bas{e^2} + Perpendicular{r^2} = Hypotenuse{e^2}} \right]\]
As we know, the sides of a square are equal to each other.
$\Rightarrow$ \[AB = BC\]
$\Rightarrow$\[{10^2} + {10^2} = A{C^2}\]
$\Rightarrow$\[100 + 100 = A{C^2}\]
$\Rightarrow$\[200 = A{C^2}\]
$\Rightarrow$\[AC = \sqrt {200} \]
$\Rightarrow$\[AC = \sqrt {2 \times 2 \times 2 \times 5 \times 5} \]
$\Rightarrow$\[AC = 2 \times 5\sqrt 2 \]
$\Rightarrow$\[AC = 10\sqrt 2 \]
Therefore, the diagonal of square will be \[10\sqrt 2 \]
Note: A square can have two diagonals. Each of the diagonal can be formed by joining the diagonally opposite vertices of a square. The properties of diagonals are as follows-
Both the diagonals are congruent (same length). Both the diagonals bisect each other, i.e. the point of joining of the two diagonals is the midpoint of both the diagonals. A diagonal divides a square into two isosceles right-angled triangles. The sum of all the internal angles of a square is equal to \[360 \circ \]and a square is a regular quadrilateral that has four equal sides and four same angles.
The diagonal of a square with side ‘a’ can be calculated using a formula \[a\sqrt 2 \]. Remember, both the diagonals of a square are equal to each other.
Complete step-by- step solution:
Given that Side of the square is \[10cm\]
In right angled\[\vartriangle ABC\]
Using Pythagoras theorem
\[A{B^2} + B{C^2} = A{C^2}\] \[\left[ {Bas{e^2} + Perpendicular{r^2} = Hypotenuse{e^2}} \right]\]
As we know, the sides of a square are equal to each other.
$\Rightarrow$ \[AB = BC\]
$\Rightarrow$\[{10^2} + {10^2} = A{C^2}\]
$\Rightarrow$\[100 + 100 = A{C^2}\]
$\Rightarrow$\[200 = A{C^2}\]
$\Rightarrow$\[AC = \sqrt {200} \]
$\Rightarrow$\[AC = \sqrt {2 \times 2 \times 2 \times 5 \times 5} \]
$\Rightarrow$\[AC = 2 \times 5\sqrt 2 \]
$\Rightarrow$\[AC = 10\sqrt 2 \]
Therefore, the diagonal of square will be \[10\sqrt 2 \]
Note: A square can have two diagonals. Each of the diagonal can be formed by joining the diagonally opposite vertices of a square. The properties of diagonals are as follows-
Both the diagonals are congruent (same length). Both the diagonals bisect each other, i.e. the point of joining of the two diagonals is the midpoint of both the diagonals. A diagonal divides a square into two isosceles right-angled triangles. The sum of all the internal angles of a square is equal to \[360 \circ \]and a square is a regular quadrilateral that has four equal sides and four same angles.
The diagonal of a square with side ‘a’ can be calculated using a formula \[a\sqrt 2 \]. Remember, both the diagonals of a square are equal to each other.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Two charges are placed at a certain distance apart class 12 physics CBSE
Difference Between Plant Cell and Animal Cell
What organs are located on the left side of your body class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
The planet nearest to earth is A Mercury B Venus C class 6 social science CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What is BLO What is the full form of BLO class 8 social science CBSE