in a rectangle longer side is twice the smaller side then ratio of longer side to its diagonal is
Answers
Step-by-step explanation:
The diagonal of the rectangle is the hypotenuse of its sides .
Let the side be x, y.
The diagonal is 3x
= (3x)2 = x2 + y2
9x 2 = x2+ y2
y2=8x2
y= 2 /2 x
The ratio of sides are x :2/2x= 1:2/2
Given,
In a rectangle, the longer side is twice the smaller side.
To find,
The ratio of the longer side to its diagonal.
Solution,
The ratio of the longer side to its diagonal will be 2:√5.
We can easily solve this problem by following thw given steps.
According to the question,
In a rectangle, the longer side is twice the smaller side.
Let's take a rectangle ABCD in which the smaller side (breadth) to is x units.
BC = AD = x units
Then,
The longer side (length) = 2x units
AB = CD = 2x units
The diagonal will be AC and BD. So, let's find the value of AC.
We know that in a rectangle all the angles are right angles.
So,
Using Pythagoras theorem in ∆ABC,
AC² = AB²+BC²
AC² = (2x)² + (x)²
AC² = 4x²+x²
AC² = 5x²
AC = √5x²
AC = x√5 units
The ratio of the longer side to its diagonal = AB:AC
Ratio = 2x:x√5
Ratio = 2:√5
Hence, the ratio of the longer side to its diagonal is 2:√5.