Question

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?

Answer 1

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

Explanation:

Answer 2

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

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 =
`(16)/(2)`

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 =
`√(4)`

I.e L - B = 2 .......2

Solving Eq 1 and 2

I.e ( L + B ) + ( L - B ) = 8 + 2

Or, 2 L = 10

∴ L =
`(10)/(2)`

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