Respuesta :
Answer:
The length of the rectangle is 54 feet .
Step-by-step explanation:
Given as :
The Area of rectangle = 770 square feet
The length is 23 feet less than 10 times its width
I.e Let The length of rectangle = L feet
And The breadth of rectangle = B feet
According to question
Length = 10 times width - 23
Or , L = 10 × B - 23
or, L = 10 B - 23
Now, Since Area of rectangle = A = Length × Breadth
Or, A = L × B
Or, 770 ft² = ( 10 B - 23 ) × B
Or, 770 = 10 B² - 23 B
Or, 10 B² - 23 B - 770 = 0
Now, solving this quadratic equation to get the value of B
Or, B = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]
or, B = [tex]\frac{23\pm \sqrt{(-23)^{2}-4\times 10\times (-770)}}{2\times 10}[/tex]
Or, B = [tex]\frac{-23\pm \sqrt{31329}}{20}[/tex]
Or, B = [tex]\frac{-23 + 177}{20}[/tex] , [tex]\frac{-23 - 177}{20}[/tex]
∴ B = 7.7 , -10
So, The breadth of the rectangle = B = 7.7 feet
So, The length of the rectangle = L = ( 10 × 7.7 - 23 )
I.e L = 54 feet
Hence The length of the rectangle is 54 feet . Answer
