Question

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

Answer 1

The function rule for the Area of Triangle is A =
`(1)/(2)` x ( 2 x - 1 ) cm²

And The area of triangle with base length 16 cm is 248 cm²

So, option A

Explanation:

Given as for a Triangle :

The measure of base of triangle = x cm

Let The height of triangle = ( 2 x - 1 ) cm

Now, Area of Triangle =
`(1)/(2)` × hight × base

Or, A =
`(1)/(2)` × ( 2 x - 1 ) cm × x cm

Or, A =
`(1)/(2)` x ( 2 x - 1 ) cm²

Again according to question :

Length of base = 16 cm

So , Height of Triangle = ( 2 x - 1 ) cm = ( 2×16 - 1 ) cm

I.e H = 31 cm

∴ Area of Triangle =
`(1)/(2)` × hight × base

or, A =
`(1)/(2)` × 31 cm × 16 cm

Or, A = 31 cm × 8 cm

I.e A = 248 cm²

Hence The function rule for the area of Triangle is A =
`(1)/(2)` x ( 2 x - 1 ) cm²

And The area of triangle with base length 16 cm is 248 cm² Answer