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If the breadth of a rectangle is 3m less than its length and its perimeter is 26m, find the length of its diagonal. If Gramfo 00​

1 Answer

2 votes

Answer:

Let's denote the length of the rectangle as

L meters and the breadth as

B meters.

According to the given information, the breadth is 3 meters less than its length, so

=

3

B=L−3.

The perimeter (

P) of a rectangle is given by the formula

=

2

(

+

)

P=2(L+B).

Given

=

26

P=26 meters:

26

=

2

(

+

(

3

)

)

26=2(L+(L−3))

Now, simplify and solve for

L:

26

=

2

(

2

3

)

26=2(2L−3)

26

=

4

6

26=4L−6

4

=

32

4L=32

=

8

L=8

Now that we know the length (

L) is 8 meters, we can find the breadth (

B):

=

3

B=L−3

=

8

3

B=8−3

=

5

B=5

5

Now, we can find the diagonal (

D) of the rectangle using the Pythagorean Theorem:

=

2

+

2

D=

L

2

+B

2

=

8

2

+

5

2

D=

8

2

+5

2

=

64

+

25

D=

64+25

=

89

D=

89

So, the length of the diagonal is

89

89

meters.

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