The area of the surface of an office desk is 15 square feet. the perimeter is 16 feet. what are the dimensions of the desk?

The dimension of the desk is Length is 5 feet and Breadth is 3 feet .

Step-by-step explanation:

Given as :

The area of the rectangular desk = 15 square feet

The perimeter of desk = 16 feet

Let The length of desk = L feet

And The breadth of desk = B feet

Now, ∵ Area of rectangle = length × breadth

I.e L × B = 15

And Perimeter of rectangle = 2 × Length +  2 × Breadth

Or, 2 × L +  2 × B = 16 feet

or L + B =

i.e L + B = 8 feet   .....1

Now , ( L - B )² = ( L + B )² - 4 ( × L × B )

or,  ( L - B )² = ( 8 )² - 4 ×( 15 )

Or,  ( L - B )² = 64 - 60

Or, ( L - B )² = 4

∴ L - B =

I.e L - B = 2      .......2

Solving  Eq 1 and 2

I.e (  L + B  ) + (  L - B ) = 8 + 2

Or, 2 L = 10

∴ L =

I.e Length = 5 feet

Put the value of L in eq 1

Or , L + B = 8

Or, B = 8 - L

Or, B = 8 - 5

∴ B = 3

I.e Breadth = 3 feet

Hence The dimension of the desk is Length is 5 feet and Breadth is 3 feet . Answer