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Which equation would best help solve the following problem? The height of a triangle is 5 m less than its base. The area of the triangle is 42 m2. Find the length of the base.

Respuesta :

mckenzieplindsay
you would do 
42=1/2*b*h
you would plug in what you know which is h=5
then you is multiply .5 by 5
which would be 2.5 then you would divide it on both sides of the equal side 
42=2.5*b
which then b would stand alone and 42/2.5 is 16.8 which would equal b so your base is 16.8m^2 

Answer with Step-by-step explanation:

Let b be the length of the base

The height of a triangle is 5 m less than its base.

i.e. height= b-5

The area of the triangle is 42 m².

We know that the area of triangle is given by:

[tex]\dfrac{1}{2}\times Base\times Height[/tex]

Here, [tex]\dfrac{1}{2}\times b\times (b-5)=42[/tex]

Multiplying by 2 on both sides, we get

b(b-5)=84

b²-5b-84=0

b²-12b+7b-84=0

b(b-12)+7(b-12)=0

(b+7)(b-12)=0

either b+7=0 or b-12=0

either b= -7 or b=12

b can't be negative so, b=12

Hence, Length of base is:

12 m

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