SOLUTION: https://vle.mathswatch.co.uk/images/questions/question2408.png please help me, thanks :)

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Question 1125382: https://vle.mathswatch.co.uk/images/questions/question2408.png
please help me, thanks :)
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

if pentagons are similar, corresponding sides are proportional; so, we have
4x%3A48=x%3A%28x%2B2%29.............solve for x
4x%28x%2B2%29=48x ...simplify
cross%284%29cross%28x%29%28x%2B2%29=cross%2848%2912cross%28x%29
%28x%2B2%29=12
x=12-2
x=10
dimensions of greater pentagon are:
4x%2Acm=4%2A10cm=40cm and 48cm
dimensions of smaller pentagon are:
x=10 and x%2B2=12
I hope you can find out what the width of the badge is.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if they're similar, then their sides are proportional.

that gets you x / 4x = (x + 2) / 48

cross multiply to get 48x = 4x * (x + 2)

simplify to get 48x = 4x^2 + 8x

subtract 48x from both sides to get 0 = 4x^2 + 8x - 48x

combine like terms to get 0 = 4x^2 - 40x

factor to get 0 = 4x * (x - 10)

solve for x to get x = 0 or x = 10

x = 0 is not good, so it has to be x = 10 or not at all.

when x = 10, the smaller figure is 10 by 12 and the larger figure is 40 by 48.

the sides are proportional, as they should be with similar figures.

10 / 40 = 12 / 48

cross multiply to get 480 = 480, confirming the ratios are equal which confirms that the sides are proportional.

your solution is that the width of the badge is 40 cm.

that's the larger pentagon that has the smaller pentagon as part of it, if i understand the problem correctly.