Question

Here are two similar pentagons which make up a badge.

4x cm

Work out the width of the badge.

|(x+2)cm 48 cm

Answer 1

Answer:

40cm

Step-by-step explanation:

Since the pentagons are similar, the corresponding sides are in the same ratio.

$\dfrac{4x}{48}=\dfrac{x}{x+2} \\\text{Cross Multiply}\\4x(x+2)=48x\\4x^2+8x=48x=0\\4x^2=48x-8x\\4x^2=40x\\4x=40\\x=10\:cm$

The width of the badge = 4x

=4 X 10

=40cm

The width of the badge is 40cm.