Question

Периметр прямоугольника равен 50 , а площадь 150 , найти большую сторону прямоугольника

Answer 1

ширина х

длина y

 

(х+y)*2=50

х*y=150 

х+y=25

y=25-х

х(25-х)=150

25х-х^2-150=0

х^2-25х+150=0

(х-10)(х-15)=0

х=10; х=15

Если х=10, то y=25-10=15

Если х=15, то y=25-15=10

Значит большая сторона прямоугольника = 15см.

Answer 2

Problem Analysis

We are given the perimeter and area of a rectangle and we need to find the length of the longer side of the rectangle.

Solution

Let's assume the length of the rectangle is a and the width is b.

We are given that the perimeter of the rectangle is 50, so we can write the equation: 2(a + b) = 50

We are also given that the area of the rectangle is 150, so we can write the equation: a * b = 150

To find the longer side of the rectangle, we need to determine which side is longer between a and b.

Let's solve the equations to find the values of a and b.

Solving the Equations

From the first equation, we can solve for a + b: 2(a + b) = 50 a + b = 25

Now, we have two equations: a + b = 25 a * b = 150

We can solve these equations using substitution or elimination.

Let's solve them using substitution. We can solve the first equation for a: a = 25 - b

Substituting this value of a into the second equation: (25 - b) * b = 150 25b - b^2 = 150 b^2 - 25b + 150 = 0

Now, we can solve this quadratic equation to find the values of b.

Quadratic Equation Solution

Using the quadratic formula, we have: b = (-(-25) ± sqrt((-25)^2 - 4 * 1 * 150)) / (2 * 1) b = (25 ± sqrt(625 - 600)) / 2 b = (25 ± sqrt(25)) / 2 b = (25 ± 5) / 2

So, we have two possible values for b: b1 = (25 + 5) / 2 = 30 / 2 = 15 b2 = (25 - 5) / 2 = 20 / 2 = 10

Now, let's substitute these values of b back into the equation a + b = 25 to find the corresponding values of a.

For b1 = 15: a + 15 = 25 a = 25 - 15 = 10

For b2 = 10: a + 10 = 25 a = 25 - 10 = 15

So, we have two possible pairs of values for a and b: (a1, b1) = (10, 15) (a2, b2) = (15, 10)

Determining the Longer Side

To determine the longer side, we compare the values of a and b.

For (a1, b1) = (10, 15): The longer side is b1 = 15.

For (a2, b2) = (15, 10): The longer side is a2 = 15.

Conclusion

The longer side of the rectangle can be either 15 or 10, depending on the orientation of the rectangle.

Please let me know if I can help you with anything else.