Question

For the area of the rectangle is 10 square inches. Determine both dimensions of the length is 8 inches les than than twice the width. A. Write an equation (in "x") to solve the problem. B. Find the solution(s).

Answer 1

x² - 4x - 5 = 0

Width of rectangle = 5 inch

Length of rectangle = 2 inch

Explanation:

Given:

Area of rectangle = 10 inch²

Length of rectangle = 2[Width of rectangle] - 8

Find:

Equation

Value of length and width

Computation;

Assume;

Width of rectangle = x

So,

Length of rectangle = 2[Width of rectangle] - 8

Length of rectangle = 2x - 8

Area of rectangle = Length × Width

10 = x(2x - 8)

2x² - 8x - 10 = 0

Divide by 2 from both side

x² - 4x - 5 = 0

x² - (5-1)x - 5 = 0

x² - 5x + x- 5 = 0

x(x - 5) + 1(x - 5)

x = 5 and x = -1

So,

Width of rectangle = 5 inch

Length of rectangle = 2x - 8

Length of rectangle = 2(5) - 8

Length of rectangle = 2 inch