Question

Найдите площадь прямоугольника диагональ которого 13 см, а сумма двух его соседних сторон 17 см.Помогите очень надо...

Answer 1

Пусть a-длина ,  b-ширина, составим систему уравнений:

a+b=17,( по условию)

a²+b²=13²;( по теореме Пифагора ( диагональ-гиппотинуза, а и б- катеты)

 

a=17-b,

(17-б)²+б²=13²; 120+2б²-34б=0; b²-17b+60=0; D=49; b= 5

 

a=17-5=12

 

S=ab=12*5=60

 

 

Answer 2

Finding the Area of a Rectangle with a Diagonal of 13 cm and the Sum of Two Adjacent Sides of 17 cm

To find the area of a rectangle with a diagonal of 13 cm and the sum of two adjacent sides of 17 cm, we can use the Pythagorean theorem and some algebraic manipulation.

Let's assume the length of one side of the rectangle is "x" cm. Since the sum of two adjacent sides is 17 cm, we can express the other side as (17 - x) cm.

According to the Pythagorean theorem, the square of the diagonal is equal to the sum of the squares of the two sides. In this case, we have:

x^2 + (17 - x)^2 = 13^2

Simplifying the equation:

x^2 + (289 - 34x + x^2) = 169

Combining like terms:

2x^2 - 34x + 120 = 0

Now, we can solve this quadratic equation to find the value of "x" using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = -34, and c = 120. Plugging in these values, we get:

x = (-(-34) ± √((-34)^2 - 4 * 2 * 120)) / (2 * 2)

Simplifying further:

x = (34 ± √(1156 - 960)) / 4

x = (34 ± √196) / 4

x = (34 ± 14) / 4

Now, we have two possible values for "x":

1. When x = (34 + 14) / 4 = 48 / 4 = 12 cm 2. When x = (34 - 14) / 4 = 20 / 4 = 5 cm

Since the length of one side cannot be smaller than the other side, we discard the second solution (x = 5 cm). Therefore, the length of one side of the rectangle is 12 cm.

Now, we can calculate the area of the rectangle by multiplying the two sides:

Area = length * width = 12 cm * (17 - 12) cm = 12 cm * 5 cm = 60 cm^2

Therefore, the area of the rectangle is 60 square centimeters.