Answer:
Height z= 2.115 cm
Explanation:
The formula for area of a trapezoid is ;
A=1/2(a+b)h where A is area, a and b are the lengths of parallel sides and h is the height of the trapezoid.
Given in the question;
A= 20 cm²
a=( 2z + 3 ) cm
b= (6z-1) cm
h= z =? unknown
Substitute in the formula as;
A=1/2(a+b)h
20=1/2(2z+3+6z-1)z -----------multiply both sides of the equation by 2
40= (2z+3+6z-1)z -----------collect like terms as
40 =(2z+6z+3-1)z
40=(8z+2)z -----open brackets as
40=8z²+2z --------- form a quadratic equation
8z²+2z-40 = 0 -----solve the quadratic equation to find value of z
z²+0.25z-5=0
z= 2.115
