the length of a rectangle is 7 inches longer than its width.If the area of the triangle is 120 square inches what are its dimensions

Answer 1

Length = 7 + Width

Width = Width

Area = (Length)(Width)

Use Substitution: 120 in² = (7 + Width)(Width)

Notice I replaced Area with "120 in²" and Length with "7+ Width" because Area is equal to 120 in² in this problem and Length in terms of the Width is given as 7 more than the Width.

Lastly, Solve for the Width as follows:

120 in² = (7 + Width)(Width) Let w = Width.

120 in² = (7 + w)(w) Simplify the right-hand side of the equation.

120 in² = w²+ 7w Subtract 120 in² from both sides of the equation.

0 = w²+7w -120 in² Factor the quadratic expression on the right-hand side of the equation.

0 = (w - 8) (w+15) Use the zero-factor property to solve for w or the width.

w = 8 or -15

Width cannot be negative. Therefore, width has to be 8 inches and length 7 more than that or 15 inches.