Question

Помогите решить задачу: Спортплощадка прямоугольной формы окружена дорожкой, ширина которой 1 м. Площадь дорожки 26м квадратных . Найдите стороны спортплощадки, если одна из них на 5м больше другой.

Answer 1

Х одна сторона площадки
х+5 другая
26÷1=26 м длина дорожки и периметр спортплощадки
2(х+х+5)=26
2(2х+5)=26
2х+5=13
2х=13-5
2х=8
х=8÷2=4 м одна сторона спортплощадки
4+5=9 м другая

Answer 2

Problem Analysis

We are given a rectangular sports field surrounded by a track with a width of 1 meter. The area of the track is 26 square meters. We need to find the dimensions of the sports field, given that one side is 5 meters longer than the other.

Solution

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

We know that the area of the track is 26 square meters. The track surrounds the sports field, so the area of the track can be calculated by subtracting the area of the sports field from the area of the rectangle formed by the outer dimensions of the track.

The area of the track is given by: Track Area = (L + 2) × (W + 2) - L × W

We are also given that one side of the sports field is 5 meters longer than the other. So we can write: L = W + 5

Substituting this value of L in the equation for the track area, we get: (W + 5 + 2) × (W + 2) - (W + 5) × W = 26

Simplifying the equation: W^2 + 7W + 10 - W^2 - 3W - 5W = 26

Combining like terms: 4W + 10 = 26

Simplifying further: 4W = 16

Dividing both sides by 4: W = 4

Substituting this value of W in the equation for L, we get: L = 4 + 5 = 9

Therefore, the dimensions of the sports field are 9 meters by 4 meters.

Answer

The dimensions of the sports field are 9 meters by 4 meters.