What is the area of a triangle whose sides are 10 meters, 14 meters, and 20 meters long? a.65 m2 b.100 m2 c. 70 m2 d.50 m2

Option A. 65 m^2

Solution:

Sides: a=10 m, b=14 m, c=20 m

Area: A=?

A=sqrt [p(p-a)(p-b)(p-c) ]

Semi-perimeter: p=(a+b+c)/2

p=(10 m+14 m+20 m)/2

p=(44 m)/2

p=22 m

A=sqrt [ (22 m)(22 m-10 m)(22 m-14 m)(22 m-20 m)]

A=sqrt [ (22 m)(12 m)(8 m)(2 m) ]

A=sqrt [ 4,224 m^4 ]

A=64.99230723 m^2

A=65 m^2

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5