Question

The length of a rectangular frame is 5cm more than the width. The area inside the frame is 66 square cm. What is the width of the frame.

Answer 1

The formula for the area of rectangle : A = l * w, where l = length and w = width.

Let x be the width of the rectangular frame in centimeters.

The length (l )of the rectangular frame = 5 cm more than the width (x ) = x + 5.

The area (A ) of the rectangular frame = 66 square cm.

To find the value of x, substitute the value of w = x, l = x + 5 and A = 66 in A = l * w.

66 = (x + 5)(x )

66 = x^2 + 5x

x^2 + 5x - 66 = 0

x^2 + 11x - 6x - 66 = 0

x (x + 11) - 6(x + 11) = 0

(x - 6)(x + 11) = 0

Apply zero poduct property : If ab = 0 then a = 0 or b = 0.

x - 6 = 0 or x + 11 = 0

x  = 6 or x = - 11

Here the positive value of x will be the considered for the width, since the measurements are never expressed with negative sign.

The width of the rectangular frame is 6 cm.