Question

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Answer 1

Answer:

3 inches

Step-by-step explanation:

Combined area is given by as equation.

(2w+8) × (2w+10) = 224

Solve this eqn.

(2w×2w) + (2w×10) + (8×2w) + (8×10) = 224

4w² + 20w + 16w + 80 = 224

4w² + 36w + 80 = 224

4w² + 36w - 144 = 0

Divide by 4 for simplification

w² + 9w - 36 = 0

Factorizing it, and we get

(w + 12) (w - 3)

From this,

w = -12 and w = 3

The negative value will not be the considerable

So, Width of the frame (w) = 3 inches

For checking, put the 'w' value in given eqn.

(2w+8) × (2w+10) = 224

[(2×3)+8] × [(2×3)+10] = 224

224 = 224