Calculate

Two friends Mário and Jano lived on two different sides of a highway. They decided to find out how wide it was. Mário drew a picture, based on which they then made measurements the next day. They measured the values ​​a =5m, b= 5.9 m, and d = 5 m. Calculate the width of the highway. Round the result to two decimal places.

Correct answer:

x =  4.8 m

Step-by-step explanation:

$$\begin{gathered} a=5\text{m} \\ b=5.9\text{m} \\ d=5\text{m} \\ s=\frac{a+b+d}{2}=\frac{5+5.9+5}{2}=\frac{159}{20}=7.95\text{m} \\ S=\sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-d)}=\sqrt{7.95\cdot (7.95-5)\cdot (7.95-5.9)\cdot (7.95-5)}\doteq 11.9092{\text{m}}^2 \\ S=\frac{a\cdot x}{2} \\ x=2\cdot S/a=2\cdot 11.9092/5=4.8\text{m} \end{gathered}$$

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