Question

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

Answer 1

Answer: AB = 2.4 cm and C'A' = 10 cm.

Step-by-step explanation: As shown in the attached figure, ΔABC is enlarged to ΔA'B'C' by a scale factor of 2.5.

Given that -  In ΔABC, CA = 4 cm  and in ΔA'B'C',  A'B' = 6 cm.

To find the length of AB and C'A'.

For doing so, we should be familiar with the definition of scale factor. It is defined as follows -

$\textup{scale~factor}=\dfrac{\textup{length of a side of the transformed figure}}{\textup{length of the corresponding side of the original figure}}.$

So,

$\textup{scale~factor}=\dfrac{A^\prime B^\prime}{AB}\\\\\Rightarrow 2.5=\dfrac{6}{AB}\\\\\Rightarrow AB=\dfrac{6}{2.5}\\\\\Rightarrow AB=2.4,$

and

$\textup{scale~factor}=\dfrac{C^\prime A^\prime}{CA}\\\\\Rightarrow 2.5=\dfrac{C^\primeA^\prime}{CA}\\\\\Rightarrow C^\prime A^\prime=2.5\times 4\\\\\Rightarrow C^\prime A^\prime=10.$.

Thus, AB = 2.4 cm and C'A' = 10 cm.