In a right triangle 13

The altitude to the hypotenuse of a right triangle is 4.8 cm. The two segments of the hypotenuse are in the ratio 4:3. Calculate the perimeter and area of the triangle.

Final Answer:

o =  24 cm
S =  24 cm²

Step-by-step explanation:

$$\begin{gathered} h=4.8\text{cm} \\ a:b=4:3 \\ {S}_1=S_2 \\ \frac{a\cdot b}{2}=\frac{c\cdot h}{2} \\ a\cdot b=c\cdot h \\ a\cdot (3/4a)=c\cdot h \\ 3/4a^2=c\cdot h \\ {a}^2+b^2=c^2 \\ {a}^2+(3/4a{)}^2=c^2 \\ {a}^2+9/16a^2=c^2 \\ 25/16a^2=c^2 \\ 5/4a=c \\ 3/4a^2=(5/4a)\cdot h \\ 3/4a=5/4\cdot h \\ 3a=5\cdot h \\ a=\frac{5}{3}\cdot h=\frac{5}{3}\cdot 4.8=8\text{cm} \\ b=\frac{3}{4}\cdot a=\frac{3}{4}\cdot 8=\frac{3\cdot 8}{4}=\frac{24}{4}=6\text{cm} \\ c=\frac{5}{4}\cdot a=\frac{5}{4}\cdot 8=\frac{5\cdot 8}{4}=\frac{40}{4}=10\text{cm} \\ o=a+b+c=8+6+10=24\text{cm} \end{gathered}$$

$$\begin{gathered} S=\frac{a\cdot b}{2}=\frac{8\cdot 6}{2}=24=24{\text{cm}}^2 \\ \text{ Verifying Solution: } \\ p=a:b=8:6=\frac{4}{3}\doteq 1.3333=4:3 \\ {c}_2=\sqrt{a^2+b^2}=\sqrt{8^2+6^2}=10\text{cm} \end{gathered}$$

Try calculation via our triangle calculator.

Try another example