Question

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.

Answer 1

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 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:

`(1)/(2)* Base* Height`

Here,
`(1)/(2)* b* (b-5)=42`

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