Triangle - is RT?

The triangle has a circumference of 90 cm. Side b is 1 cm longer than side c, and side c is 31 cm longer than side a. Calculate the length of the sides and determine whether a triangle is a right triangle.

Result

a =  9 cm
b =  41 cm
c =  40 cm
p=

Yes

No

Step-by-step explanation:

$$\begin{gathered} b=1+c \\ c=31+a \\ a+b+c=90 \\ a+(1+c)+c=90 \\ a+1+2c=90 \\ a+1+2(31+a)=90 \\ a+1+2\cdot (31+a)=90 \\ 3a=27 \\ a=\frac{27}{3}=9 \\ a=9=9\text{cm} \end{gathered}$$

$$\begin{gathered} c=31+a=31+9=40 \\ b=1+c=1+40=41\text{cm} \end{gathered}$$

$$\begin{gathered} c^2=a^2+b^2 \\ 41^2=40^2+9^2 \\ p=1 \end{gathered}$$

Try calculation via our triangle calculator.

Try another example