Find the length a diagonal of a rectangle having sides 11 cm and 60 cm.
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 2.3 | Page 44
Find the length a diagonal of a rectangle having sides 11 cm and 60 cm.
According to Pythagoras theorem,
In ∆ABC
\[{AB}^2 + {BC}^2 = {AC}^2 \]
\[ \Rightarrow \left( 60 \right)^2 + \left( 11 \right)^2 = {AC}^2 \]
\[ \Rightarrow 3600 + 121 = {AC}^2 \]
\[ \Rightarrow {AC}^2 = 3721\]
\[ \Rightarrow AC = 61 cm\]
Hence, the length of a diagonal of the rectangle is 61 cm.
Explanation:-
We can use the Pythagorean theorem to find the length of the diagonal of a rectangle having sides 11 cm and 60 cm.
According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two sides are the length and the width of the rectangle, and the diagonal is the hypotenuse. So we have:
diagonal^2 = length^2 + width^2
Substituting the values given in the problem, we get:
diagonal^2 = 11^2 + 60^2 diagonal^2 = 121 + 3600 diagonal^2 = 3721
Taking the square root of both sides, we get:
diagonal = sqrt(3721) diagonal = 61
Therefore, the length of the diagonal of the rectangle is 61 cm (rounded to the nearest whole number).
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 2.3 | Page 44