Practice Set 2.1 | Q 8 | Page 39
Find the diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.
Solution
According to Pythagoras theorem, in ∆ABC
[{AB}^2 + {BC}^2 = {AC}^2 ]
[ Rightarrow {35}^2 + {12}^2 = {AC}^2 ]
[ Rightarrow 1225 + 144 = {AC}^2 ]
[ Rightarrow {AC}^2 = 1369]
[ Rightarrow AC = 37 cm]
Hence, the length of the diagonal is 37 cm.
Explanation:-
Given that we have a right triangle ABC with hypotenuse AC, where AB = 35 cm and BC = 12 cm.
We can use Pythagoras theorem which states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.
Applying Pythagoras theorem in ∆ABC, we get: AB² + BC² = AC² 35² + 12² = AC² 1225 + 144 = AC² 1369 = AC² Taking square root on both sides, we get: AC = 37 cm
Hence, the length of the diagonal AC is 37 cm.
Chapter 2 – Pythagoras Theorem- Text Book Solution
Practice Set 2.1 | Q 8 | Page 39