The area of a triangle is 21ft². If the height of the triangle is 7ft, how long is the base of the triangle? Please give your answer and explain how you found it.

The answer is b = 6

Step-by-step explanation:

Area of a triangle= 1/2 × b × h

A = 21, h = 7, b = ?

21 = 1/2 × b × 7 (multiplying through)

21 = 7b/2

Cross multiply

2 × 21 = 7b

42 = 7b

b = 42/7

b = 6

b = 6ft

Step-by-step explanation:

Area of a triangle = 1/2 x base x height

Given the area = 21ft^2

Height = 7ft

Base = ?

Using the above formula

21 = 1/2 x b x 7

21 = 7b/2

Cross multiply

7b = 21 x 2

7b = 42

Divide both sides by 7

7b/7 = 42/7

b = 6ft

The length of the base is 6ft

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!