Paolo was asked to find the original dimension of an enlarged pentagon. His solution is shown next to the pentagons. A small pentagon has a bottom side length of x centimeters and left side length of 3 centimeters. A larger pentagon has a bottom side length of 8 centimeters and left side length of 12 centimeters. Write a proportion. StartFraction 3 over 12 EndFraction = StartFraction x over 8 EndFraction Cross multiply. 8 x = 36 Solve for x. x = 4.5 Not drawn to scale What error did Paolo make in his solution?
Answers
Given :
A small pentagon has a bottom side length of x centimeters and left side length of 3 centimeters. A larger pentagon has a bottom side length of 8 centimeters and left side length of 12 centimeters.
To Find : the original dimension of an enlarged pentagon.
Write a proportion.
Solution:
enlarged pentagon
bottom side length of 8 cm
left side length = 12 cm
Original pentagon
bottom side length of x cm
left side length = 3 cm
Corresponding sides will be in the same proportion
=> x/8 = 3/12
=> 12x = 24
=> x = 2
bottom side length of original pentagon = 2 cm
Paolo did : 3/12 = x/8
36 = 8x ( in this step rather than cross multiply he multiplied on same side which was division)
=> x = 4.5
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