Width

[Guest]

A wooden plaque (square) had a metal inlay (square) in the center, with a wooden strip of uniform width around the metal square. The ratio of the metal area is 25 to 39 to the wooden area. Determine width (in inches) of the wooden strip.

Let x = side of entire plaque.
y = side length of inlay.
w = width of wooden strip.

Area of square = s^2

Area of plaque = x^2

of inlay = y^2

Unsure how to proceed.

Image attached.

[Guest]

The problem is a problem of units, we are not given any particular size of the square.
If we use inches units.

Ratio of "metal inner square" to "wood outer strip" is "25 square units" to "39 square units"

Area of inner square = 25 sq.units so length of sides of inner = sq root of 25 = 5 units

Area of outer strip = 39 sq. units. Total area of plaque = 39 + 25 = 64 sq units

Length of outer edge = sq. root 64 = 8 units

So width of strip = (8 - 5) / 2 = 1.5 units.

So if working in inches the width of strip = 1.5 inches.

If working in feet width of strip = 1.5 feet.

The ratios of the areas remains the same.

[Guest]

Ok, thanks again.