10. The length and width of a rectangle are (x 4) cm and x cm respectively. A square has the same perimeter as this rectangle. If you add the areas of the rectangle and the square, the result is 94cm2. Solve for x.
The length and width of a rectangle are (x + 4) cm and x cm respectively. the perimeter of this rectangle is 2(x + 4) + 2x = 4x + 8. The square is of the same perimeter, so its side is 1/4(4x + 8) = x + 2. [ The rectangle area = x(x + 4), and the square area = (x + 2)^2. We were give their area sum is 94, that is x(x+4)+(x+2)^2=94, solve the equation x^2+4x+x^2+4x+4=94, 2x^2+8x-90=0, x^2+4x-45=0, (x+9)(x-5)=0, x = -9 (impossible) or x = 5. ]
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