Question

ABC DEF and their areas be respectively 64 cm 2 and 121 cm 2 .If EF = 15.4 cm, Find BC.

Answer 1

Formula:

$\bigg( \dfrac{\text{length 1}}{\text{length 2}} \bigg)^2 = \dfrac{\text{Area 1}}{\text{Area 2}}$

.

Plugged in the known variables and find the length BC:

$\bigg( \dfrac{\text{BC}}{15.4} \bigg)^2 = \dfrac{\text{64}}{\text{121}}$

.

Square root both sides:

$\dfrac{\text{BC}}{15.4} = \sqrt{\dfrac{\text{64}}{\text{121}} }$

$\dfrac{\text{BC}}{15.4} = \dfrac{8}{11}$

.

Cross multiply:

$11 \times \text {BC} = 8 \times 15.4$

$11 \times \text {BC} = 123.2$

.

Divide both sides by 11:

$\text {BC} = 123.2 \div 11$

$\text {BC} = 11.2$

.

Answer: BC = 11.2 cm

Answer 2

$\frak {\underline{\orange{Answer}}}$

Area of ∆ ABC = 64 cm²

Area of ∆ DEF = 121 cm²

We know that :-

∆ ABC $\sim$ ∆ DEF

We also know :-

$\sf \frac{ar(ABC)}{ar(DEF)} = {(\frac{AB}{DE} )}^{2}= {(\frac{BC}{EF} )}^{2}={(\frac{AC}{DF} )}^{2}$

$\sf \frac{64}{121} = { (\frac{(BC)}{(15.4)}) }^{2}$

$\sf \frac{BC}{15.4} = \sqrt{ \frac{64}{121} }$

$\sf \frac{BC}{15.4} = \frac{8}{11}$

$\sf BC = \frac{8}{11} \times 15.4$

$\boxed{\purple{\sf{ BC = 11.2}}}$

BC = 11.2 cm