Isosceles triangle sides

Calculate the size of the base and side of an isosceles triangle if the side is 1 cm longer than the base and the height to the base is 2 cm shorter than the side.

Final Answer:

z =  16 cm
r =  17 cm

Step-by-step explanation:

$$\begin{gathered} r=z+1\text{cm} \\ h=r-2\text{cm} \\ {r}^2=h^2+(z/2{)}^2 \\ {r}^2=(r-2{)}^2+((r-1)/2{)}^2 \\ -0.25r^2+4.5r-4.25=0 \\ 0.25r^2-4.5r+4.25=0 \\ a=0.25;b=-4.5;c=4.25 \\ D=b^2-4ac=4.5^2-4\cdot 0.25\cdot 4.25=16 \\ D>0 \\ {r}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{4.5\pm \sqrt{16}}{0.5}=9\pm 4\sqrt{4} \\ {r}_{1,2}=9\pm 8 \\ {r}_1=17 \\ {r}_2=1 \\ r=r_1=17\text{cm} \\ z=r-1=17-1=16\text{cm} \end{gathered}$$

Our quadratic equation calculator calculates it.

$$\begin{gathered} r=r_1=17=17\text{cm} \\ \text{ Verifying Solution: } \\ h=\sqrt{r^2-(z/2{)}^2}=\sqrt{17^2-(16/2{)}^2}=15\text{cm} \end{gathered}$$

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