Question

Triangles ABC and DEF are similar.

(i) If area ($△ABC$)= 16 ${\text{cm}}^2$, area($△$ DEF)= 25 ${\text{cm}}^2$ and $BC=2.3\text{cm}$, find $EF$.

(ii) If area ($△ABC$)= 9 ${\text{cm}}^2$, area($△$ DEF) = 64 ${\text{cm}}^2$ and $DE=5.1\text{cm}$, find $AB$.

(iii) If $AC=19\text{cm}$ and $DF=8\text{cm}$, find ratio of the area of two triangles.

(iv) If area ($△ABC$)= 36 ${\text{cm}}^2$, area ($△$ DEF) =64 ${\text{cm}}^2$ and $DE=6.2\text{cm}$, find $AB$.

(v) If $AB=1.2\text{cm}$ and $DE=1.4\text{cm}$, find the ratio of the areas of triangle $ABC$ and $DEF$.

Answer 1

1.)given ABC and DEF are similar

therefore square of the ratio of sides =ratio of areas

implies $\left(\sqrt{\frac{16}{25}}\right)=\frac{BC}{EF}$

therefore $EF=\frac{11.5}{4}=2.875$ $\because BC=2.3$

2.) according to above

$\left(\sqrt{\frac{64}{9}}\right)=\frac{DE}{AB}$

therefore $AB=\frac{15.3}{8}=1.9125$ $\because DE=5.1$

3.)RATIO OF TRIANGLES =$(\frac{19}{8}{)}^2$ = $5.640625$

4.)$\left(\sqrt{\frac{64}{36}}\right)=\frac{DE}{AB}$

$\therefore AB=4.65$ $\because DE=6.2$

5.)ratio of areas of $ABC$ and $DEF$ =${\left(\frac{1.2}{1.4}\right)}^2$ = $0.605042017$