Question

A rectangle has an area of 12x²+17x-5mm². For what value of x is the rectangle a square? What is the area of a square? Justify your answer and show your work. A=12x²+17x-5mm²

Answer 1

23mm

528 mm^2

Explanation:

The area of a rectangle is given as the product of its length and width.

Given that 12x²+17x-5mm² is the area

factorize

12x²+17x-5 = 12x²+20x -3x-5

= 4x(3x+5)-1(3x+5)

= (3x+5)(4x-1)

For the rectangle to be a square, it means that the sides 3x+ 5 and 4x - 1 are equal. Hence

3x + 5 = 4x -1

collect like terms

3x - 4x = -5 -1

-x = -6

x = 6

substitute into the sides

3x + 5 = 3(6) + 5 = 23

4x -1 = 4(6) - 1 = 23

The area of the square which is a product of the sides

= 23 * 23

= 529