One side 3

One side of a triangular banner is 1 1/2 times longer than the second side and 2 cm shorter than the third side. The perimeter of the triangle is 98 cm. How long is the shortest side?

Final Answer:

b =  24 cm

Step-by-step explanation:

$$\begin{gathered} r=1\frac{1}{2}=1+\frac{1}{2}=\frac{1\cdot 2+1}{2}=\frac{2+1}{2}=\frac{3}{2}=1.5 \\ o=98\text{cm} \\ a=r\cdot b \\ a=c-2 \\ a+b+c=o \\ b<a;b<c \\ r\cdot b+b+(r\cdot b+2)=o \\ 1.5\cdot b+b+(1.5\cdot b+2)=98 \\ 4b=96 \\ b=\frac{96}{4}=24=24\text{cm} \\ b=24 \\ \text{ Verifying Solution: } \\ a=r\cdot b=\frac{3}{2}\cdot 24=\frac{3\cdot 24}{2}=\frac{72}{2}=36\text{cm} \\ c=a+2=36+2=38\text{cm} \end{gathered}$$

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