A rectangle frame needs to be constructed so that its width and length are in a ratio of 3:4 and its diagonal is 25 inches. What is the perimeter of the frame?

70 inches

Step-by-step explanation:

From the diagram attached,

Assuming the width, lenght and diagonal of the rectangle forms a right angle triangle.

Applying pythagoras theorem,

a² = b²+c²................... Equation 1

Where a = diagonal =  25 inches, b = width = 3x inches, c = length = 4x inches

Substitute these values into equation 1 and solve for x

25² = (4x)²+(3x)²

625 = 14x²+9x²

625 = 25x²

25x² = 625

x² = 625/25

x² = 25

x = √25

x = 5 inches.

Therefore,

Width(w) = 3×5 = 15 inches

Length(l) = 4×5 = 20 inches

Perimeter (P) = 2(l+b)

P = 2(15+20)

P = 2(35)

P = 70 inches

Hence the perimeter of the frame is 70 inches

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