Question

The width of a rectangle is 5 inches less than its length. If the rectangle has an area 104in^2 what are its length and width?

Answer 1

Answer:

Length = 13 inches

Width = 8 inches

Step-by-step explanation:

Given----> Width of a rectangle is 5 inches less than its length and area of rectangle is 104 inch²

To find ----> Area of rectangle .

Solution-----> Let length of rectangle be x

ATQ,

Width of rectangle = Length of rectangle - 5

=> Width of rectangle = ( x - 5 )

Area of rectangle = length × width

=> 104 = x ( x - 5 )

=> 104 = x² - 5x

=> x² - 5x - 104 = 0

Now we factorize it by splitting the middle term ,

=> x² - ( 13 - 8 ) x - 104 = 0

=> x² - 13x + 8x - 104 = 0

=> x ( x - 13 ) + 8 ( x - 13 ) = 0

=> ( x - 13 ) ( x + 8 ) = 0

If x + 8 = 0

=> x = - 8 ( impossible )

If x - 13 = 0

=> x = 13

So , length = x

= 13 inch

Width = x - 5

= 13 - 5

= 8 inches

Additional information----->

1) Perimetre of rectangle = 2 ( l + b )

2) Area of square = side²