Question

Высоты параллелограмма равны 4 и 6 см, а его периметр - 40 см. Найти острый угол параллелограмма.

Answer 1

Параллелограмм АВСД.
АВ=а, ВС=b
Р=2(а+b)=40  --->  a+b=20  ---> b=20-a
BH перпенд. АД,  BH=4
ВК перпенд. СД ,  ВК=6
ΔАВН:  sin<BAD=BH/AB=4/a
ΔBCK:  sin<BCK=BK/BC=6/(20-a)
<BAD=<BCK  --->  $\frac{4}{a}=\frac{6}{20-a}$

$4(20-a)=6a\\\\80-4a=6a\\\\10a=80\\\\a=8\\\\sin\ \textless \ BAD=\frac{4}{8}=\frac{1}{2}\; \; \Rightarrow \; \; \ \textless \ BAD=30^\circ$

Answer 2

Finding the Height of the Parallelogram

To find the height of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. In this case, the base is one of the sides of the parallelogram, and the area is equal to the product of the base and the height.

Let's denote the base of the parallelogram as b and the height as h. We are given that the base is 4 cm and the area is 6 cm. Therefore, we can set up the equation:

b * h = 6

Substituting the given values, we have:

4 * h = 6

Solving for h, we find:

h = 6 / 4 = 1.5 cm

Therefore, the height of the parallelogram is 1.5 cm.

Finding the Perimeter of the Parallelogram

To find the perimeter of the parallelogram, we need to know the lengths of all four sides. However, we are only given the lengths of two sides, which are 4 cm and 6 cm. Without additional information, we cannot determine the exact lengths of the other two sides or the angles of the parallelogram.

Conclusion

Based on the given information, we can find the height of the parallelogram, which is 1.5 cm. However, we cannot determine the exact value of the acute angle of the parallelogram or the lengths of the other two sides without additional information.