General
General
Easy
Question
Given a square with side length of 12√2 cm, find the diagonal.
- 24 cm
- 20 cm
- 18 cm
- 22 cm
Hint:
We are given the length of a side of the square. It is 12√2. We are asked to find the length of the its hypotenuse in cm. The diagonal joins the two opposite corners of the square. If divides the square into two triangles. For this question, we will consider one of the two triangles. It is a right-angled triangle.
The correct answer is: 24 cm
Let one of triangles be ABC
Such that, angle ABC is 90°.
AC is the diagonal and the hypotenuse.
The square has all sides equal. So, the triangle is an isosceles triangle.
So, AB = BC
We will use the Pythagoras theorem. It states that, the square of the hypotenuse is equal to the sum of square of the two sides.
AC2 = AB2 + BC2
= (12√2)2 + (12√2)2
= 288 + 288
= 576
Taking the square root we get,
AC = 24
Therefore, the length of the diagonal is 24cm.
For such questions, we should know the properties of different triangles.
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