MATH SOLVE

3 months ago

Q:
# The area of a triangle whose height is 1 more than 6 times its base is 13 square feet. If the base of the triangle is x feet, which equation models this situation?

Accepted Solution

A:

We must know that the are of the triangle is given by definition by

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

where

b = base

h = height

Substituting the values

A = (1/2) * (x) * (1 + 6x)

A = (1/2) * (x + 6x ^ 2)

Since the area is 13 then

(1/2) * (x + 6x ^ 2) = 13

Clearing x we have

6x ^ 2 + x = 26

6x ^ 2 + x-26 = 0

(x-2) * (x + 13/6) = 0

As we look for the base of a triangle then x> 0

x = 2

answer

the base is x = 2

6x ^ 2 + x = 26

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

where

b = base

h = height

Substituting the values

A = (1/2) * (x) * (1 + 6x)

A = (1/2) * (x + 6x ^ 2)

Since the area is 13 then

(1/2) * (x + 6x ^ 2) = 13

Clearing x we have

6x ^ 2 + x = 26

6x ^ 2 + x-26 = 0

(x-2) * (x + 13/6) = 0

As we look for the base of a triangle then x> 0

x = 2

answer

the base is x = 2

6x ^ 2 + x = 26