The area of a rectangle is (x2 + 5x - 14) sq. cm. Neither its length nor width has a measure of 1 inch. What are its dimensions if they can be expressed as factors of the area?

Question

Factoring General Trinomials subject

Answer 1

x^2+5x-14=x^2+7x-2x-14=x(x+7)-2(x+7)=(x-2)(x+7)

Length=x+7  cm

Breadth=x-2  cm

Answer 2

x²+5x-14=(x+7)(x-2), so the length=x+7, width=x-2. These factors must be positive so x>2cm. The width must exceed 1cm, therefore x-2>1, x>3cm. So, for example, if x=4cm, length=11cm and width=2cm.

Length>10cm, width>1cm. The difference between length and width is always 9cm.