Question

Спортивная площадка имеет форму прямоугольника.Если его длину и ширину увеличить на 3м то его площадь увеличится на 144м2.Если его длину уменьшить на 12м а ширину на 2м,то его площадь уменьшится на 146м^2.Найдите размеры площадки УРАВНЕНИЕМ ЛИБО СИСТЕМОЙ.ЗАРАНЕЕ СПАСИБО!

Answer 1

Problem Analysis

We are given a rectangular sports field. If we increase its length and width by 3 meters, the area increases by 144 square meters. If we decrease the length by 12 meters and the width by 2 meters, the area decreases by 146 square meters. We need to find the dimensions of the field using an equation or a system of equations.

Solution

Let's assume the original length of the sports field is L meters and the original width is W meters.

According to the given information, if we increase the length and width by 3 meters, the area increases by 144 square meters. This can be represented by the equation:

(L + 3)(W + 3) = LW + 144 Similarly, if we decrease the length by 12 meters and the width by 2 meters, the area decreases by 146 square meters. This can be represented by the equation:

(L - 12)(W - 2) = LW - 146 We can solve this system of equations to find the values of L and W.

Let's expand and simplify equation LW + 3L + 3W + 9 = LW + 144

Simplifying further, we get: 3L + 3W = 135 Similarly, let's expand and simplify equation LW - 12L - 2W + 24 = LW - 146

Simplifying further, we get: -12L - 2W = -170 Now we have a system of equations: 3L + 3W = 135 -12L - 2W = -170 We can solve this system of equations using any method, such as substitution or elimination.

Let's solve it using the elimination method. We can multiply equation by 2 and equation by 3 to eliminate the variable W:

6L + 6W = 270 -36L - 6W = -510 Adding equations and we get: -30L = -240

Dividing both sides by -30, we find: L = 8

Substituting the value of L into equation we can find the value of W: 3(8) + 3W = 135 24 + 3W = 135 3W = 111 W = 37

Therefore, the dimensions of the sports field are 8 meters by 37 meters.

Answer

The dimensions of the sports field are 8 meters by 37 meters.