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100.
If the area of the trapezoid is
(d + b) x c, then what is a in terms
of b?

A. 26
B. b
C. b + 2
D. 2b + 2

100 If the area of the trapezoid is d b x c then what is a in terms of b A 26 B b C b 2 D 2b 2 class=

Respuesta :

Check the picture below.

so our bases are "d" and "d+a+b", and a height of "c".

[tex]\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(x+y)}{2}~~ \begin{cases} x,y=\stackrel{parallel~sides}{bases}\\ h~~~=height\\ \cline{1-1} x=d\\ y=d+a+b\\ h=c\\ A=(d+b)c \end{cases}\implies (d+b)c=\cfrac{c[d+(d+a+b)]}{2} \\\\\\ 2(d+b)c=c[d+(d+a+b)]\implies 2dc+2bc=c(2d+a+b)[/tex]

[tex]\bf ~~\begin{matrix} 2dc \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+2bc=~~\begin{matrix} 2dc \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+ac+bc\implies 2bc=ac+bc\implies 2bc=c(a+b) \\\\\\ \cfrac{2b~~\begin{matrix} c \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} c \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}=a+b\implies 2b=a+b\implies 2b-b=a\implies \blacktriangleright b=a \blacktriangleleft[/tex]

Ver imagen jdoe0001

The value of the variable 'a' in terms of 'b' will be a = b. Then the correct option is B.

What is a trapezoid?

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.

If the area of the trapezoid is (d + b) · c.

Then the value of the variable 'a' in terms of 'b' will be

We know that the area of a trapezoid is given as,

A = 1/2(Sum of parallel sides) x Height

Then the equation will be

(d + b) · c = (1/2)·(d + d + a + b) · c

Simplify the equation, then we have

2d + 2b = 2d + a + b

          a = b

The value of the variable 'a' in terms of 'b' will be a = b.

Then the correct option is B.

More about the trapezoid link is given below.

https://brainly.com/question/22607187

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