Given :
Triangle ABC and QRS are similar
BC=15, AB=18, RQ=12 and SQ=15.
a)
We know that in similar triangles, the corresponding angles are proportional.
[tex]\frac{BC}{RS}=\frac{BA}{RQ}=\frac{AC}{SQ}[/tex]
Substitute BC=15, AB=18, RQ=12 and SQ=15, we get
[tex]\frac{15}{RS}=\frac{18}{12}=\frac{AC}{15}[/tex]
[tex]\text{ Consider }\frac{15}{RS}=\frac{18}{12}\text{ to find RS.}[/tex]
Taking reciprocal on both sides, we get
[tex]\text{ }\frac{RS}{15}=\frac{18}{12}[/tex]
Multiplying by 15 on both sides, we get
[tex]\text{ }\frac{RS}{15}\times15=\frac{18}{12}\times15[/tex]
we know that 15/15=1.
[tex]\text{ }RS=\frac{18}{12}\times15[/tex]
Multiplying 18 and 15, we get
[tex]\text{ }RS=\frac{270}{12}[/tex]
Dividing 270 by 12, we get
[tex]\text{ }RS=22.5[/tex][tex]\text{ Consider }\frac{12}{18}\text{ =}\frac{AC}{15}\text{to find AC.}[/tex]
Multiplying by 15 on both sides, we get
[tex]\frac{12}{18}\times15\text{ =}\frac{AC}{15}\times15[/tex]
[tex]\frac{180}{18}\text{=}AC[/tex][tex]AC=10[/tex]
Hence AC=10 and RS=22.5.
b)
The perimeter of the triangle = the sum of all three sides.
The perimerter of ABC is
[tex]P_1=15+18+10=43[/tex]
The perimeter of QRS is
[tex]P_2=15+12+22.5=49.5[/tex]
The ratio of the parameter is
[tex]\frac{P_1}{P_2}=\frac{43}{49.5}=\frac{430}{495}=\frac{86}{99}[/tex]
The ratio is 86:99
If the given triangles are congruent
BC=SQ=15
AB=RS=18
AC=RQ=12
Hence RS=18 and AC=12.
The perimeter of ABC=15+18+12=45
The perimeter of QRS=15+18+12=45
The ratio of the perimeter is
45/45
Hence the ratio is 1:1.
