Question
A square has side length 95. Calculate the length of the diagonal of the square. Express your answer in simplest radical form.
- 134.4
- 67.2
- 95√2
- (95√2)/2
Hint:
We are given the length of side of a square. It is 95. We are asked to find the length of the diagonal. 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: 95√2
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
= (95)2 + (95)2
= 2(95)2
Taking the square root of both the sides.
AC = 95√2
Therefore, the length of the diagonal is 95√2.
For such questions, we should know properties of square and right-angled triangle.
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