pleasee help!!!6

Question

A rectangular , 4cm longer than it is wide, has a diagonal 20 cm long, How to write and solve a quadratic equation to determine of the rectangular,sollve by factoring by completeng the square or by using quadratic formula not by graphing . make sure you give the dimensions of the rectangular for the final answer.

Answer 1

Let width of rectangle w = x cm

Length is 4 cm longer than it is wide

Length of rectangle l = (x+4) cm

Diagonal of rectangle d = 20 cm

Length , width , Diagonal are forms right angled triangle.

Length² + width² = Diagonal²

(x+4)² + x² = 20²

x² + 8x + 16 + x² = 400

2x² + 8x + 16 - 400 = 0

2x² + 8x - 384 = 0

x² + 4x - 192 = 0

For factoring above equation, appropriate factor is 192 = 12×16

x²  + 16x - 12x - 192 = 0

x ( x + 16 ) - 12 ( x  + 16 ) = 0

( x + 16 ) ( x - 12 ) = 0

By using zero product property : If AB = 0 then A = 0 , B = 0

( x + 16 ) = 0  and  ( x - 12 ) = 0

( x + 16 ) = 0 then x = -16 is invalid.Since negative dimensions are not exists.

( x - 12 ) = 0 then  x = 12 cm is valid

Width of rectangle w = 12 cm

Length of rectangle l = (12+4) = 16 cm

Final Answer :

The dimensions of the rectangle :  Width is 12 cm , Length is 16 cm