Question

Периметр треугольника abc равен 280мм. ab больше bc на 2 см, а сторона ac меньше стороны ab на 30 мм. найдите площадь квадрата равный стороне bc ответ запишите в см кв

Answer 1

AB+BC+AC=28
AB=x
BC=2x
AC=2x-2
x+2x+2x-2=28
5x=30
x=6
AB=6
BC=12
AC=10

Answer 2

Perimeter of Triangle ABC

To find the perimeter of triangle ABC, we need to know the lengths of its three sides: AB, BC, and AC. The problem statement provides some information about the lengths of these sides.

Let's denote the length of side AB as x, the length of side BC as y, and the length of side AC as z.

According to the problem statement: - AB is greater than BC by 2 cm: AB = BC + 2 cm. - AC is smaller than AB by 30 mm: AC = AB - 30 mm.

We also know that the perimeter of a triangle is the sum of the lengths of its sides. So, the perimeter of triangle ABC can be calculated as follows: Perimeter = AB + BC + AC.

To find the values of AB, BC, and AC, we can use the given information and solve the equations.

Let's substitute the values of AB and AC in terms of BC into the perimeter equation: Perimeter = (BC + 2 cm) + BC + (BC - 30 mm).

Now, we can simplify the equation by converting the units to a common one. Let's convert 30 mm to cm: 30 mm = 3 cm.

Substituting the values and simplifying the equation: Perimeter = 3BC + 2 cm - 3 cm.

Simplifying further: Perimeter = 3BC - 1 cm.

We are given that the perimeter of triangle ABC is 280 mm. To convert this to cm, we divide by 10: 280 mm = 28 cm.

Now, we can set up the equation: 28 cm = 3BC - 1 cm.

Solving for BC: 3BC = 28 cm + 1 cm, 3BC = 29 cm, BC = 29 cm / 3, BC ≈ 9.67 cm.

Area of the Square

The problem asks us to find the area of a square that has a side length equal to BC.

The area of a square is given by the formula: Area = side length * side length.

Substituting the value of BC into the formula: Area = BC * BC.

Using the value of BC we found earlier: Area = 9.67 cm * 9.67 cm.

Calculating the area: Area ≈ 93.67 cm².

Therefore, the area of the square with a side length equal to BC is approximately 93.67 cm².

Please let me know if you need any further assistance!