The area of the square is 144cm. The perimeter of a rectangle is equal to the perimeter of a square. The length of a rectangle is 12 more than the breadth of a rectangle. Find the ratio between the diagonal of a square and the diagonal of a rectangle.
1. √5 : √2
2. 2 : √5
3. √2 : √5
4. 2 : 5
5. √5 : 2
1. √5 : √2
2. 2 : √5
3. √2 : √5
4. 2 : 5
5. √5 : 2
Correct Answer – Option 2 : 2 : √5
Given:
⇒ Side of a square = √144 = 12cm
Using pythgoras theorem,
⇒ Diagonal of a square = √288 = 12√2cm
⇒ Perimeter of rectangle = 2(length + breadth) = 4 × 12 = 48cm
⇒ Length = 12 + breadth
Solving,
⇒ Length = 18cm and Breadth = 6cm
Using pythagoras theorem,
⇒ Diagonal of rectangle = √360 = 6√10cm
∴ Required ratio = 12√2 : 6√10 = 2 : √5