Answer:
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 = [tex]\frac{16}{2}[/tex]
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 = [tex]\sqrt{4}[/tex]
I.e L - B = 2 .......2
Solving Eq 1 and 2
I.e ( L + B ) + ( L - B ) = 8 + 2
Or, 2 L = 10
∴ L = [tex]\frac{10}{2}[/tex]
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
