Question

the height of a triangle is 1 cm less than twice the length of the base. let x = the length of the base

Answer 1

x = the lenght of the base
2x = twice the lenght of the base
2x-1 = 1cm less than twice the lenght of the base

Area of the triangle is the product of half of base and the hight


`A=\frac12x\cdot(2x-1)\\\\A=x^2-\frac12x`

Answer 2

A. A=12x(2x−1);248cm2

Explanation:

The complete question is

The height of a triangle is 1 cm less than twice the length of the base. Let x = the length of the base. Write a function rule for the area of the triangle and determine the area if the length of its base is 16 cm.

A. A=12x(2x−1);248cm2

B. A=12xh;128cm2

C. A=12x(x−2);112cm2

D. A=122x(x−1);240cm2

The area of a triangle is defined as

`A=(bh)/(2)`

Where
`b` is the base and
`h` is the height.

According to the problem, the height is 1 cm less than twice the base, that is

`h=2b-1`

Now, replacing the second relation in the area equation, we have

`A=(bh)/(2)=(b(2b-1))/(2)\\A=(2b^(2)-b)/(2)`

If
`b=16` we have

`A=(2b^(2)-b)/(2)=(2(16)^(2)-16)/(2)\\A=248`

So, the area is 248 square centimeters.

Therefore, the right answer is A.