Question

Gelo makes up a problem for the trapezoid SHDO with bases SH and DO, nd median WA, where SH =8-x, WA =x +2 and OD = 3x -4. The problem ask for the value of x.

Answer 1

To find the value of x in the given trapezoid SHDO, we use the formula for the median of a trapezoid and solve the resulting equation.

Step-by-step explanation:

We are given a trapezoid SHDO with bases SH and DO, and the median WA. The lengths of SH, WA, and DO are given by SH = 8 - x, WA = x + 2, and DO = 3x - 4, respectively. To find the value of x, we can set up an equation using the properties of a trapezoid:

WA = (SH + DO) / 2

Substituting the given values, we have:

x + 2 = (8 - x + 3x - 4) / 2

Simplifying the equation:

x + 2 = (7x + 4) / 2

Multiplying both sides of the equation by 2 to eliminate the fraction:

2x + 4 = 7x + 4

Subtracting 2x from both sides:

4 = 5x

Dividing both sides by 5:

x = 4/5 = 0.8