Given a triangle ABC with area 1cm² and another triangle ABC with area of 9cm². Find the length AB if length AB is 4cm where A'B'C is the image of ABC under an enlargement.

Tunajua kuwa uwiano wa maeneo ya pembetatu mbili zinazofanana ni sawa na mraba wa kipimo cha ukuzaji.

$$\frac{\text{Eneo la } A'B'C'}{\text{Eneo la } ABC} = k^2$$ $$\frac{9 \text{ cm}^2}{1 \text{ cm}^2} = k^2$$ $$9 = k^2$$

Ili kupata $k$, tunachukua mzizi wa mraba wa pande zote mbili:

$$k = \sqrt{9}$$ $$k = 3$$

Tunajua kuwa uwiano wa urefu wa pande zinazolingana ni sawa na kipimo cha ukuzaji.

$$\frac{\text{Urefu wa } A'B'}{\text{Urefu wa } AB} = k$$

Tunapewa urefu wa $A'B'$ ni $4 \text{ cm}$ na tumepata $k=3$.

$$\frac{4 \text{ cm}}{AB} = 3$$

Ili kupata $AB$, tunapanga upya mlinganyo:

$$AB = \frac{4 \text{ cm}}{3}$$ $$AB = \frac{4}{3} \text{ cm}$$

Urefu wa AB ni:

$$\frac{4}{3} \text{ cm}$$