The diagonal of a rectangle is thrice its smaller side. The ratio of

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The diagonal of a rectangle is thrice its smaller side. The ratio of the length to the breadth of the rectangle is:

A. 3 : 1
B. √3 ∶1
C. √2 ∶1
D. 2√2 ∶1
E. None of these

MayankSingh · Answer

IMO D

Let ABCD be the rectangle with breadth AB= "b"
Length= BC ; Diagonal AC= 3b
In right angled triangle ABC,

AC^2 = AB^2 + BC^2
=> BC = Sqrt (3b^2- b^2) = 2b sqrt2
 Req Ratio, BC/AB= 2srt2 : 1

Rishikasaini2807 · Answer

D
l^2 + b^2 = (3b)^2

(l/b)^2 = 8/1

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Babineaux · Answer

In a Rect. let L and B be the length and breath respectively,
And B be the smaller side.

Now diagonal is  sqrt (L ^2  + B ^2 )

As per given condition  sqrt (L ^2  + B ^2 ) = 3B

Equating both sides we get (L/B) ^2  = 8/1
Thus L : B = 2  sqrt(2)  : 1

IMO ans is D

sambitspm · Answer

Kindly see the attachment. 
D

NiftyNiffler · Answer

The diagonal of a rectangle is thrice its smaller side. The ratio of the length to the breadth of the rectangle is:

A. 3 : 1
B. √3 ∶1
C. √2 ∶1
D. 2√2 ∶1
E. None of these

Let's say length = x , breadth = y

Diagonal = 3y

x^2 + y^2 = (3y)^2 
=> x = 2*\sqrt{2}y

Ratio of sides = 2*\sqrt{2}:1

So, the answer is  D

Saasingh · Answer

IMO D

A diagonal is the hypotenuse and therefore we can say that :

L² + B² = (3B)²
--> L² = 8B²
--> L/B = 2 root 2

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exc4libur · Answer

d=3x
x^2+y^2=d^2
x^2+y^2=(3x)^2
y^2=9x^2-x^2=8x^2;
√y^2/√x^2=√2^3x^2/√x^2
2x√2/x=2√2/1

Ans (D)

monikakumar · Answer

l be the length, b shortest side breadth, d diagonal
 d^2=l^2+b^2

d=3b (given)

on substituiting,
l= 2\sqrt{2} 
 \frac{l}{b}=\frac{2\sqrt{2}}{1}

Ans D

Abi1995 · Answer

Ans - D

We get below

Using information

Under root of (l2+ b2)= 3b
L2 + b2= 9b^2

Divide by b^2 in LHS
(L/B)^2 + 1 = 9

(L/B) ^ 2 = 8

(L/B)= 2_/2 : 1

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Jawad001 · Answer

The diagonal of a rectangle is thrice its smaller side. The ratio of the length to the breadth of the rectangle is:

A. 3 : 1
B. √3 ∶1
C. √2 ∶1
D. 2√2 ∶1
E. None of these

Solution:
The smaller side (Breadth) of the rectangle = x units
The diagonal of the rectangle = 3x units
The length = 2√2 x units
Therefore, the ratio of length to breath = 2√2 x : x = 2√2 :1 
Answer: D

hemantbafna · Answer

Length=l, breadth=b,diagonal=d

d=3b

In a rectangle;
(3b)^2=(b)^2+(l)^2
(9b)^2-(b)^2=l

l:b=8(b)^2/b=8/1=2√2 ∶1
 D

The diagonal of a rectangle is thrice its smaller side. The ratio of

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The diagonal of a rectangle is thrice its smaller side. The ratio of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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