Question

Katie wants to hang a painting in a gallery. The painting and frame must have an area of 45 square feet. The painting is 6 feet wide by 7 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?a. 4x^2 + 26x + 45 = 0b. 4x^2 + 26x − 3 = 0c. x^2 + 13x − 3 = 0d. x^2 + 13x + 45 = 0

Answer 1

Answer:

$4x^2+26x-3 = 0$

Step-by-step explanation:

Given that the total area of Frame and Painting is 45 Sq Fts.

Dimensions of painting are 6 feet and 7 feet. Hence.

Let us assume the uniform thickness of frame is x

Hence the Length of frame with painting = 7+2x

and breadth = 6+2x

Area of the frame = length * breadth

$45=(7+2x)(6+2x)\\45=42+14x+12x+4x^2\\45=42+26x+4x^2\\4x^2+26x+42-45\\4x^2+26x-3=0$

Hence option b is correct.