Question

Площа трапеції дорівнює 120 см2, а її висота - 8см. Знайди основи трапеції, якщо одна з них на 6 см більша за іншу.

Answer 1

S=(a+b)*h/2

h-высота, a, b -основания

a=b+6

120=(2b+6)*6/2

120=6*(b+3)

20=b+3

b=17

a=17+6=23

Answer 2

Finding the Bases of a Trapezoid

To find the bases of the trapezoid, we can use the formula for the area of a trapezoid, which is given by the equation:

A = (1/2) * (a + b) * h

Where: - A is the area of the trapezoid - a and b are the lengths of the bases - h is the height of the trapezoid

Given: - The area of the trapezoid is 120 cm^2 - The height of the trapezoid is 8 cm - One base is 6 cm longer than the other base

We can use this information to solve for the lengths of the bases.

Calculating the Bases

Let's denote the lengths of the bases as x and x + 6 (since one base is 6 cm longer than the other).

We can use the given area and height to solve for the lengths of the bases. Substituting the given values into the formula for the area of a trapezoid, we get:

120 = (1/2) * (x + (x + 6)) * 8

Solving for x:

120 = (1/2) * (2x + 6) * 8

120 = 4x + 24

4x = 120 - 24

4x = 96

x = 24

So, one base is 24 cm, and the other base is 24 + 6 = 30 cm.

Therefore, the lengths of the bases of the trapezoid are 24 cm and 30 cm.