Find perimeter of a square if its diagonal is [10sqrt{2}]
10 cm
[40sqrt{2}]cm
20 cm
40 cm
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 1.5 | Page 43
Some question and their alternative answer are given. Select the correct alternative.
Find perimeter of a square if its diagonal is [10sqrt{2}]
10 cm
[40sqrt{2}]cm
20 cm
40 cm
solution
It is given that ABCD is a square.
∴ AB = BC = CD = DA = x (say)
According to Pythagoras theorem, in ∆ABD
[{text{AB}}^2 + {text{AD}}^2 = {text{BD}}^2 ]
[ Rightarrow x^2 + x^2 = left( 10sqrt{2} right)^2 ]
[ Rightarrow 2 x^2 = 200]
[ Rightarrow x^2 = 100]
[ Rightarrow x = sqrt{100}]
[ Rightarrow x = 10 text{cm}]
Hence, the side of the square is 10 cm.
Now,
Perimeter of a square = [4 times left( side right)]
=[4 times x]
=[4 times 10]
=[40]
Hence, the correct option is 40 cm.
Explanation:-
The problem involves finding the perimeter of a square when the length of its diagonal is known. It is given that ABCD is a square and all its sides are equal, i.e., AB = BC = CD = DA = x. Using Pythagoras theorem in ∆ABD, we get:
AB^2 + AD^2 = BD^2 x^2 + x^2 = (10√2)^2 (since BD = 10√2, as given in the problem) 2x^2 = 200 x^2 = 100 x = √100 x = 10 cm
Hence, the side of the square is 10 cm. To find the perimeter of the square, we use the formula:
Perimeter of a square = 4 x (side)
Substituting the value of x, we get:
Perimeter of the square = 4 x 10 = 40
Therefore, the perimeter of the square is 40 cm.
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 1.5 | Page 43