Question
A square has diagonal length 13 m. Find the side length of the square, in centimeters, rounded to two decimal places.
- 9.19
- 18.38
- 5.10
- 13
Hint:
We are given the length of a diagonal of the square. It is 13m. We are asked to find the length of the its side 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: 9.19
Let one of triangles be ABC
Such that, angle ABC is 90°.
AC is the diagonal and the hypotenuse.
AC = 13m
The square has all sides equal. So, the triangle is an isosceles triangle.
So, AB = BC
Let the side of the square be denoted as "s".
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
132 = s2 + s2
169 = 2s2
Dividing both the sides by 2 we get,
2s2 = 169
s2 = 84.5
s = 9.19
Therefore, the length of the sides of a square is 9.19.
For such questions, we should know the properties of triangle and square.
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