# Math

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The length and width of a rectangle are (x+4)cm and xcm respectively. Write down expressions for:
A. The perimeter of the rectangle
B. The length of the side of a square with the same perimeter
If the sum of the areas of the square and the rectangle is 94cm(square), find x
Pls include workings thx

• Math -

p = 2(width+length) = 2(x+4+x) = 2(2x+4) = 4x+8

s = p/4 = (4x+8)/4 = x + 2

94 = x(x+4) + (x + 2)^2
94 = x^2 + 4x + x^2 + 4x + 4
94 = 2x^2 + 8x + 4
2x^2 + 8x - 90 = 0
x^2 + 4x - 45 = 0
(x+9)(x-5) = 0
x = 5

rectangle is 5x9; p=28 a=45
square = 7x7; p=28 a=49
45+49 = 94

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