Question

you have a 5-inch by 7-inch picture that you framed. When you hung the picture, you found that the entire area is 69.56 in. What is the width of the frame?​

Answer 1

Answer:  d) 2.4 inches

Step-by-step explanation:

Let x represent the width of the frame

Then the area of the frame is:

(x + 5)(x + 7) = 69.56

Rewrite it in Standard form of a quadratic equation:

x² + 12x + 35 = 69.56

x² + 12x - 34.56 = 0

Use Quadratic Formula to solve for x:

$x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-12+\sqrt{12^2-4(1)(-34.56)}}{2(1)}\\\\\\x=\dfrac{-12+\sqrt{282.24}}{2}\\\\\\x=\dfrac{-12+16.6}{2}\\\\\\x=\dfrac{4.8}{2}\\\\\\x=\large\boxed{2.4}$

Answer 2

Answer:

d. 2.4 in

Step-by-step explanation:

So initially w/o frame the area was 5 x 7 = 35 sq in.

Now we have to add the width of the frame to both dimensions.

(5+w)(7+w) = 69.56 sq in

35 + 7w + 5w + w² = 69.56

w² + 12w + 35 = 69.56

w² + 12w - 34.56 = 0

I use the quadratic formula to solve this (x = -b±√b²-4ac / 2a). I cheat by using a quadratic program on the calculator :,)

w = 2.4

w = -14.4

Since we can't have a negative width, the answer must be w = 2.4 inches.

You can also just plug the answer choices one-by-one into the calculator with guess-and-check because this is multiple choice.