Question

Mikaela placed a frame around a print that measures 10 inches by 10 inches. The area of just the frame itself is 69 square inches. What is the width of the frame?

Answer 1

Answer:

1.5 in

Step-by-step explanation:

Let x be the width of the frame.

Side of print=10 in

Area of frame=69 square in

We have to find the width of the frame.

Side of frame=10+x+x=10+2x

Area of square=$(side)^2$

By using the formula

Area of print=$10\times 10=100in^2$

Area of frame with print=$(10+2x)^2$

Area of frame=Area of frame with print-Area of print

$69=(10+2x)^2-100$

$(10+2x)^2=69+100=169$

$(10+2x)=\sqrt{169}=\pm 13$

$10+2x=13$

Because Side is always positive.

$2x=13-10=3$

$x=\frac{3}{2}=1.5$

Hence, width of frame=1.5 in

Answer 2

   Width of the frame around the square print having sides 10 inches will be 1.5 inches.

Area of a square shape:

• Area of a square is given by the expression,

          Area = (length of a side)²

Given in the question,

•  Dimensions of the print = 10 inches by 10 inches
•  Area of the frame around the print = 69 square inches

Let the width of the frame around the print = x inches

Therefore, length of the frame including print = (10 + 2x) inches

And the width of the frame including print = (10 + 2x) inches

Area of the frame including print = (10 + 2x)²

Now, area of the frame = Area of the frame including print - Area of the print

69 = (10 + 2x)² - (10)²

69 = 100 + 4x² + 40x - 100

69 = 4x² + 40x

4x² + 40x - 69 = 0

4x² + 46x - 6x - 69 = 0

2x(2x + 23) - 3(2x + 23) = 0

(2x - 3)(2x + 23) = 0

x = -11.5, 1.5

     Since, width of the frame can not be negative, width of the frame will be 1.5 inches.

Learn more about the area of the cylinder surrounded by a thick wall here,

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