​ The area of a rectangle is {75}cm^(2) The length of the rectangle is (√2 +5). Calculate the width of the rectangle​

Question

​

The area of a rectangle is

`{75}cm^(2)`
The length of the rectangle is (√2 +5). Calculate the width of the rectangle​

Answer 1

Let the width of the rectangle be w. Then we have:

`lw = 75`

`w(√(2) + 5) = 75`

`w = (75)/(√(2) + 5)`

Multiplying both the numerator and denominator by
`√(2) - 5`, we get:

`w = (75(√(2) - 5))/((√(2) + 5)(√(2) - 5))`

Simplifying the denominator, we get:

`w = (75(√(2) - 5))/(-1)`

`w = -75√(2) + 375`

Therefore, the width of the rectangle is approximately 264.1 cm.

Answer 2

`width = (75*(5-√(2))/(23)`

Explanation:

To find the width of the rectangle, divide the area by the length.

`Width = (area)/(length)`

`=(75)/(√(2)+5)\\\\\\\text{To rationalize, multiply the denominator and the numerator by } \ √(2)-5`

`=(75* (5 - √(2)))/((5+√(2))(5-√(2)))\\\\\\=(75*(5-√(2)))/(5^2 - (√(2))^2)\\\\\\=(75(5-√(2)))/(25-2)\\\\\\=(75*(5-√(2)))/(23)`