Question

The perimeter of a rectangle is numerically equal to its area. If the width of a rectangle is 2 ³/₄ cm. , then its length is ________. ​

Answer 1

Answer:

Let the length of rectangle be l and width be b ,

b = 11/4

Area of rectangle = l×b

Perimeter of rectangle = 2(l + b)

Now,

According to question,

\begin{gathered} 2(l + b) = l \times b \\ \\ 2(l + \frac{11}{4} ) = l \times \frac{11}{4} \\ \\ 2l + \frac{11}{2} = \frac{11l}{4} \\ \\ 2l - \frac{11l}{4} = - \frac{11}{2} \\ \\ \frac{8l - 11l}{4} = - \frac{11}{2} \\ \\ - \frac{3l}{4} = - \frac{11}{2} \\ \\ l = - \frac{11}{2} \times - \frac{4}{3} \: \\ \\ l = \frac{22}{3} \ \ cm \end{gathered}

2(l+b)=l×b

2(l+

4

11

)=l×

4

11

2l+

2

11

=

4

11l

2l−

4

11l

=−

2

11

4

8l−11l

=−

2

11

−

4

3l

=−

2

11

l=−

2

11

×−

3

4

l=

3

22

cm

[/tex]

Step-by-step explanation:

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