Question

A triangle ABC has been enlarged by scale factor k = 2.5 to the triangle A' B' C'.

Calculate:

(i) the length of AB, if A' B' = 6cm.

(ii) the length of C'A' if CA= 4cm.

• A. AB = 2.4 cm
• B. AB = 2.5 cm
• C. C'A' = 12 cm
• D. C'A' = 10 cm

Answer 1

Answer: (A), (D)

The correct options are
A

AB = 2.4 cm

D

C'A' = 10 cm

Scale factor(k) = 2.5

$△ABC$ is enlarged to $△A^{\prime }{B}^{\prime }{C}^{\prime }$

(i) A' B'= 6 cm

We have

$\frac{A^{\prime }{B}^{\prime }}{AB}=2.5$

$\frac{6}{AB}=2.5$

$AB=\frac{6}{2.5}$ = 2.4 cm

(ii) CA= 4 cm

$\frac{C^{\prime }{A}^{\prime }}{CA}=2.5$

$\frac{C^{\prime }{A}^{\prime }}{4}=2.5$

$\therefore C^{\prime }{A}^{\prime }=10cm$