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

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

So, option A

Step-by-step 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 = × hight × base

Or, A =   ×  ( 2 x - 1 ) cm × x cm

Or, A =   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 = × hight × base

or, A = × 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 =   x ( 2 x - 1 ) cm²  

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

∠cbe and ∠deb are same-side interior angles.

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