Awindow frame has a length of (5x+3) inches an a width of (x+6) inches. the area of the glass in the window is (4x^2+26x+15) square inches. what is the area of the trim around the glass in the window? a-(9x^2+33x+59) square inches b-(x^2+3x+7) square inches c-(9x^2+59+33) d-(x^2+7x+3)

ANSWER

the area of the trim around the glass in the window is option ( D)

i.e (x²+7x+3)

REASON

As given in the question

A window frame has a length of (5x+3) inches an a width of (x+6) inches.

As the shape of the window in the form of rectangle.

Formula

Area of the rectangle = length × breadth

put the value in the above equation

we get

Area of window =  (5x+3)× ( x + 6)

                         =  5x² + 33x + 18 inches²

As given in the question

The area of the glass in the window is (4x²+26x+15) square inches.

Area trim around the glass in the window = area of the window - area of the glass.

put the value

we get

= (  5x² + 33x + 18 ) - ( 4x²+26x+15)

= 1x²+ 7x + 3  inches²

therefore the correct option is (D)

Hence proved