Question

A rectangle has an area of 234 cm2 and a perimeter of 62 cm. What are its dimensions? It's length is ? Its width is? where length > width

Answer 1

Answer:

Length of the rectangle is  18 cm

and  Width is 13 cm.

Step-by-step explanation:

Here, let us assume the length of the rectangle  a cm

and the width of the rectangle  = b cm

Now, Perimeter of the Rectangle = 2 (length + Width) = 62 cm

⇒ 2( a+ b )  = 62 cm

Area of the Rectangle =  (length x Width) = 234 sq. cm

⇒ a x b  =  234 sq. cm

Now, taking both the equations and simplifying for a and b , we get:

2( a+ b )  = 62   ⇒  (a + b) = 31 or, b = 31  -a

  ab  =  234

Substitute b = (31-a)  in second equation

 ab  =  234  ⇒  a (31-a) = 234

or, $31 a  - a^2 = 234\\\implies a^2 - 31a + 234 = 0\\a^2 - 13 a - 18 a + 234 = 0\\\implies (a-13)(a-18) =0\\\implies a  = 13, a = 18$

Now, if a  = 13, b = 31 - 13  =  18 cm

and if a = 18,    b = 31 - 18 = 13 cm

But, given Length > Width ⇒ a > b ⇒ a = 18 cm, b = 13 cm

Hence, the length of the rectangle is  18 cm and  Width is 13 cm.