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A triangle ABC has been enlarged by scale factor m = 2.5 to the triangle A’ B’ C’ Calculate: (i) the length of AB, if A’ B’ = 6 cm. (ii) the length of C’ A’ if CA = 4 cm.

Given that, \[\Delta \text{ }ABC\]has been enlarged by scale factor \[m\text{ }of\text{ }2.5\text{ }to\text{ }\Delta \text{ }ABC\]

(i) \[AB\text{ }=\text{ }6\text{ }cm\]

So,

\[AB\left( 2.5 \right)\text{ }=\text{ }AB\text{ }=\text{ }6\text{ }cm\]

\[AB\text{ }=\text{ }2.4\text{ }cm\]

 

(ii) \[CA\text{ }=\text{ }4\text{ }cm\]

Hence,

\[CA\left( 2.5 \right)\text{ }=\text{ }CA\]

\[CA\text{ }=\text{ }4\text{ }x\text{ }2.5\text{ }=\text{ }10\text{ }cm\]