Question

S трапеции 320 сантиметров в квадрате, H(высота) трапеции равна 8 сантиметров . Найти основание трапеции если длина одного из оснований составляет 60% длины другого

Answer 1

Дано
S=320cm^2  .h=8cm. a, b- основания,  
найти b, если a=0.6b
S=(a+b)/2*h
(0.6b+b)/2*8=320
1.6b=80
b=50(cm)

Answer 2

Finding the Base of a Trapezoid

To find the base of a trapezoid when the area and height are given, we can use the formula:

Area (S) = (a + b) / 2 * h where: - S is the area of the trapezoid, - a and b are the lengths of the bases of the trapezoid, and - h is the height of the trapezoid.

In this case, we are given that the area of the trapezoid is 320 square centimeters (S = 320 cm²) and the height is 8 centimeters (h = 8 cm). We need to find the length of one of the bases (a or b) when the length of one base is 60% of the length of the other base.

Let's solve this step by step:

1. Let's assume the length of one base is x. Since the length of the other base is 60% of x, the length of the other base can be represented as 0.6x.

2. Using the formula for the area of a trapezoid, we can substitute the given values:

S = (a + b) / 2 * h 320 = (x + 0.6x) / 2 * 8

3. Simplifying the equation:

320 = (1.6x) / 2 * 8 320 = 0.8x * 8 320 = 6.4x

4. Solving for x:

x = 320 / 6.4 x = 50

Therefore, the length of one base of the trapezoid is 50 centimeters.

Answer: The length of one base of the trapezoid is 50 centimeters.