Posted by **Simon** on Sunday, October 23, 2011 at 9:27am.

The length and width of a rectangle are (x+4) cm and x cm 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 94 cm^2 , find x. Explain your working and solution

- Math -
**Reiny**, Sunday, October 23, 2011 at 9:40am
a) P = 2(x+4) + 2x = 4x + 8

b) if this had been a square, then each side would have been (4x+8)/4 = x+2

x(x+4) + (x+2)^2 = 94

x^2 + 4x + x^2 + 4x + 4 = 94

2x^2 + 8x - 90 = 0

x^2 + 4x - 45 = 0

(x+9)(x-5) = 0

x = a negative or x = 5

check:

rectange was 5 by 9 for an area of 45

square was 7 by 7 for an area of 49

total area is 45+49 = 94 ,

all is good!

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