The perimeter of two similar triangles ABC and PQR are respectively, 48 cm and 36 cm. If PQ = 12 cm, then find AB. About the author Clara
GIVEN:- The perimeter of two similar triangles ABC and PQR are respectively, 48 cm and 36 cm. If PQ = 12 cm, then find AB. TO FIND:- [tex] \small \mathsf{ \color{navy}{AB}}[/tex] FINAL SOLUTION:- [tex]YOU’VE \: \: TO \: FIRST \: \: TAKE \: TWO \: \\ SIMILAR \: \: TRIANGLES[/tex] [tex]\huge{ \color{purple}{ \colorbox{grey}{SO,}}}[/tex] [tex]\bold\pink{†PQ/AB†}[/tex] [tex]\bold\pink{†BC/QR†}[/tex] [tex]\bold\pink{†PR/AC=48/36†}[/tex] [tex] \small{ \textsf{ \textbf{ \color{lime}{GIVEN IF, PQ=12cm}}}}[/tex] [tex]\orange{\bold{\underbrace{\overbrace{then}}}}[/tex] [tex]48 \times 12 \\ \: \: \: \: \: \: \: \: \: \: \: – \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 36 \: \: \: [/tex] [tex]\huge\tt\colorbox{aqua}{=13.3 or 16 cm}[/tex] Reply
Answer: AB = 16cm Step-by-step explanation: Since the ratio of the corresponding sides of similar triangles is same as the ratio of their perimeters. ∴ ∆ABC ~ ∆PQR =>$\fbox{${\frac{AB}{PQ}\mathrm{{=}}\frac{BC}{QR}\mathrm{{=}}\frac{AC}{OR}\mathrm{{=}}\frac{\mathrm{48}}{\mathrm{36}}}$}$ => $\fbox{${\frac{AB}{PQ}\mathrm{{=}}\frac{\mathrm{48}}{\mathrm{36}}}$}$ =>$\fbox{${\frac{AB}{\mathrm{12}}\mathrm{{=}}\frac{\mathrm{48}}{\mathrm{36}}}$}$ [tex]ab = \frac{48 \times 12}{36} cm \\ = > 16cm.[/tex] [tex] {}^{i \: hope \: its \: help \: you} [/tex] Reply
GIVEN:-
The perimeter of two similar triangles ABC and PQR are respectively, 48 cm and 36 cm. If PQ = 12 cm, then find AB.
TO FIND:-
[tex] \small \mathsf{ \color{navy}{AB}}[/tex]
FINAL SOLUTION:-
[tex]YOU’VE \: \: TO \: FIRST \: \: TAKE \: TWO \: \\ SIMILAR \: \: TRIANGLES[/tex]
[tex]\huge{ \color{purple}{ \colorbox{grey}{SO,}}}[/tex]
[tex]\bold\pink{†PQ/AB†}[/tex]
[tex]\bold\pink{†BC/QR†}[/tex]
[tex]\bold\pink{†PR/AC=48/36†}[/tex]
[tex] \small{ \textsf{ \textbf{ \color{lime}{GIVEN IF, PQ=12cm}}}}[/tex]
[tex]\orange{\bold{\underbrace{\overbrace{then}}}}[/tex]
[tex]48 \times 12 \\ \: \: \: \: \: \: \: \: \: \: \: – \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 36 \: \: \: [/tex]
[tex]\huge\tt\colorbox{aqua}{=13.3 or 16 cm}[/tex]
Answer:
AB = 16cm
Step-by-step explanation:
Since the ratio of the corresponding sides of similar triangles is same as the ratio of their perimeters.
∴ ∆ABC ~ ∆PQR
=>$\fbox{${\frac{AB}{PQ}\mathrm{{=}}\frac{BC}{QR}\mathrm{{=}}\frac{AC}{OR}\mathrm{{=}}\frac{\mathrm{48}}{\mathrm{36}}}$}$
=> $\fbox{${\frac{AB}{PQ}\mathrm{{=}}\frac{\mathrm{48}}{\mathrm{36}}}$}$
=>$\fbox{${\frac{AB}{\mathrm{12}}\mathrm{{=}}\frac{\mathrm{48}}{\mathrm{36}}}$}$
[tex]ab = \frac{48 \times 12}{36} cm \\ = > 16cm.[/tex]
[tex] {}^{i \: hope \: its \: help \: you} [/tex]