Question

A rectangle has a length of 23 feet less than 10 times it’s width . If the area of the rectangle is 770 square feet find the length

Answer 1

The length of the rectangle is 54 feet .

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 =
`\frac{-b\pm \sqrt{b^(2)-4* a* c}}{2* a}`

or, B =
`\frac{23\pm \sqrt{(-23)^(2)-4* 10* (-770)}}{2* 10}`

Or, B =
`(-23\pm √(31329))/(20)`

Or, B =
`(-23 + 177)/(20)` ,
`(-23 - 177)/(20)`

∴ 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