Answer:
[tex]\sf x = \dfrac{32}{3} \ cm[/tex]
Step-by-step explanation:
Similar polygons:
Two polygons are similar if they have same number of sides, corresponding angles are congruent, and their corresponding sides are in same proportion.
If the ratio of the corresponding sides of two similar polygons is a: b, then the ratio of the area is a²: b².
Let the length of the side of larger polygon be 'x' cm.
Ratio of sides = 8: x
Ratio of areas = 8²: x²
= 64: x²
It is given the area of similar polygons are 27 cm² and 48 cm²
64 :x² = 27: 48
[tex]\sf \dfrac{64}{x^2}=\dfrac{27}{48}\\\\\\Cross \ multiply,\\\\x^2 *27 = 48*64\\\\x^2 = \dfrac{48*64}{27}\\\\x^2= \dfrac{16*64}{9}\\\\\\x^2=\dfrac{4^2*8^2}{3^2}\\\\x^2 =\left(\dfrac{4*8}{3}\right)^2\\\\x^2=\left(\dfrac{32}{3}\right)^2[/tex]
Take square root both sides,
[tex]\sf x = \dfrac{32}{3}\\\\[/tex]
