Question

Площа трап. =24см2 а висота 4см . знайти основи трап. ,якщо вони відносяться як 1:5

Answer 1

S=(a+b)/2 * h
S = (x+5x)/2 * 4 = 24
12x=24
x=2

S = (2+10)/2 * 4 = 24

Answer 2

Calculating the Bases of a Trapezoid

To find the bases of the trapezoid when the area is 24 cm^2 and the height is 4 cm, and they are in the ratio of 1:5, we can use the formula for the area of a trapezoid:

Area of a trapezoid = (1/2) * (sum of the bases) * (height)

We also know that the bases are in the ratio of 1:5. Let's denote the smaller base as x and the larger base as 5x.

Using the given area and height, we can set up the equation:

24 = (1/2) * (x + 5x) * 4

Solving for x will give us the value of the smaller base, and then we can find the larger base by multiplying x by 5.

Calculation

Using the given equation, we can solve for x:

24 = (1/2) * (x + 5x) * 4

Simplify the equation: 24 = (1/2) * 6x * 4

24 = 12x

Divide both sides by 12: x = 2

Now that we have the value of x, we can find the larger base: 5x = 5 * 2 = 10

Answer

The bases of the trapezoid are: - 2 cm (smaller base) - 10 cm (larger base)