length of diagonal of square is √2cm , find the length of its side .
Answers
Answer:
This is a 45-45-90. If one of the leg is x, then the hypotenuse must be x times the square root of two. So, let me find a leg. (Remember, this a square, so all the sides are congruent, thus the two legs are congruent)
2s^2=s^2+4s+4
-s^2 -s^2
s^2= 4s+4
-4s. -4s Since I am going to use the quadratic
s^2-4s=4 formula, I am moving all the terms to
-4 -4 one side of the equation.
s^2-4s-4= 0 So, a=1, b=-4, c=-4
You might recall the quadratic formula. I am going to do what is inside the radical sign, which is called the Determinant. The determinant can be found by using
b^2-4ac I am sure you remember. Now, substitute
(-4)^2-(4)(1)(-4) the values of a,b and c.
16-(-16)= 32 This 32 goes underneath the radical sign
Next, I am going to substitute for a and b. So, we have
[-(-4)+/-(sq.rt. of 32)]/2(1)
[4+/-(sq.rt of 32)]/2 The sq.rt. of 32, can be
[4+/-(4 times sq.rt of 2)/2 simplified as sq.rt 16
times sq.rt. 2 or
4 times sq.rt.2
[2+/-(2 sq.rt 2] Simplifying by
dividing by 2.
Now, we have two possible answers for x, the length of legs
x= 2+2sq.rt 2. or x= 2-2sq.rt. 2
This can't be an
answer. Legs can't be negative.
So, each leg is 2+2 times sq.rt 2. Since this is a 45-45-90 right triangle, we can find the hypotenuse by multiplying the leg by sq.rt.2. Let's do that,
(2+2sq.rt.2)(sq.rt.2)= 2 sq.rt.2+4
Note that when you multiply sq.rt. 2 times sq.rt. 2, our answer is 2. So, we have 2*2=4. That's where we got the 4 just in case you are wondering.
The legs are each (2+2 sq.rt. 2) and the hypotenuse is 2 sq.rt.2+4.
Step-by-step explanation:
diagonal of square=√2×side
10=√2×side
10upon √2=side
10 × √2 upon. √2×√2 = side
10√2 upon 2 = side
side =5√2