Question

The sides of a rectangle are in the ratio 6 : 8, find the smaller side of the rectangle if its diagonal is 100 cm


1) 80cm

2) 60cm

3) 12cm

4) 16cm​

Answer 1

Given:-

• Ratio of the sides of rectangle = 6 : 8
• Diagonal of the rectangle = 100 cm

To Find:-

The length of smaller side.

Assumption:-

Let the Ratio constant be x

Hence Ratio = 6x : 8x

Solution:-

We have,

Length = 6x

Breadth = 8x

We know,

Diagonal of a rectangle = $\sf{\sqrt{(length)^2 + (breadth)^2}}$

Hence,

$\sf{ 100 = \sqrt{(6x)^2 + (8x)^2}}$

= $\sf{100 = \sqrt{36x^2 + 64x^2}}$

= $\sf{100 = \sqrt{100x^2}}$

= $\sf{100 = 10x}$

= $\sf{x = \dfrac{100}{10}}$

= $\sf{x = 10\:cm}$

Putting the values of x in the length and breadth,

Length = 6x = $\sf{6\times 10 = 60\:cm}$

Breadth = 8x = $\sf{8\times 10 = 80\:cm}$

Here we can clearly see that side length is smaller than side breadth. Hence the length of smaller side is 60 cm.

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Verification!!

Let us verify whether the answer we got is correct or not.

We will put the values of length and breadth in the formula of diagonal of a rectangle and will see whether the result comes as 100 cm or not.

Hence,

$\sf{\sqrt{(length)^2 + (breadth)^2}}$

= $\sf{\sqrt{(60)^2 + (80)^2}}$

= $\sf{\sqrt{3600 + 6400}}$

= $\sf{\sqrt{10000}}$

= $\sf{100}$

Hence we got the result as 100 cm as per given in the question.

Hence the answer we got is correct [Verified].

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Important:-

• The formula of diagonal of a rectangle is $\sf{\sqrt{(length)^2 + (breadth)^2}}$

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Answer 2

Answer:

Given, the length and breadth of a rectangle are in the ratio 3:2 respectively.

Then let the length and breadth of the rectangle be 3x,2x respectively.

If the sides of the rectangle are extended on each side by 1 m then length and breadth will be 3x+1 m and 2x+1 m.

According to the problem,

2x+1

3x+1

=

7

10

or, 20x+10=21x+7

or, x=3.

So length and breadth are 9,6 m respectively.

Now area of the rectangle be 9×6=54 m

2

.