27 cm2 : 57 cm2 = 18 cm : 38 cm
Goal: Check if the two ratios are equal by simplifying each one.
Simplify the first ratio: (27 ext{cm}^2 : 57 ext{cm}^2)
Write it as a fraction:
(displaystyle rac{27 ext{cm}^2}{57 ext{cm}^2})
Same units cancel:
(displaystyle rac{27}{57})
Divide top and bottom by (3) (HCF is (3)):
(displaystyle rac{27 div 3}{57 div 3} = rac{9}{19})
Simplify the second ratio: (18 ext{cm} : 38 ext{cm})
Write it as a fraction:
(displaystyle rac{18 ext{cm}}{38 ext{cm}})
Same units cancel:
(displaystyle rac{18}{38})
Divide top and bottom by (2):
(displaystyle rac{18 div 2}{38 div 2} = rac{9}{19})
Conclusion: Both ratios simplify to (displaystyle rac{9}{19}). Therefore, they are equal. The statement is true.