A polygon of area A=400cm2 is mapped onto a polygon of area A=400cm2. Find x if the corresponding length is 10cm. 4) Two cuboids A and B have corresponding length 15mm and 20mm respectively. Find the volume of B given that the volume of A = 19.2mm3.

Tunajua kuwa uwiano wa maeneo ya poligoni zinazofanana ni sawa na mraba wa kipimo cha ukuzaji ($k$).

$$\frac{\text{Eneo la poligoni iliyopangwa}}{\text{Eneo la poligoni asili}} = k^2$$ $$\frac{1600 \text{ cm}^2}{400 \text{ cm}^2} = k^2$$ $$4 = k^2$$

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

$$k = \sqrt{4}$$ $$k = 2$$

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

$$\frac{\text{Urefu wa upande unaolingana (poligoni iliyopangwa)}}{\text{Urefu wa upande unaolingana (poligoni asili)}} = k$$ $$\frac{x}{10 \text{ cm}} = 2$$

Ili kupata $x$, tunazidisha pande zote mbili kwa $10 \text{ cm}$:

$$x = 2 \times 10 \text{ cm}$$ $$x = 20 \text{ cm}$$

Thamani ya $x$ ni:

$$20 \text{ cm}$$