# Two patches

Peter taped the wound with two rectangular patches (one over the other to form the letter X).
The area sealed with both patches at the same time had a content of 40cm2 and a circumference of 30cm. One of the patches was 8cm wide.
What was the width of the second patch?

Result

v2 =  4 cm

#### Solution:

$S = 40 \ cm^2 \ \\ o = 30 \ cm \ \\ v_{ 1 } = 8 \ cm \ \\ \ \\ \ \\ S = a v_{ 1 } = b v_{ 2 } \ \\ o = 2(a+b) \ \\ \ \\ a = S/v_{ 1 } = 40/8 = 5 \ cm \ \\ \ \\ b = o/2- a = 30/2- 5 = 10 \ \\ \ \\ v_{ 2 } = S/b = 40/10 = 4 \ cm = 4 \ \text{ cm }$

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