Question

Find the Base & Height of the triangle

Area =42 in^2

Answer 1

Base: 14 and height: 6 OR Base: -12 and height -7

Explanation:

First, set up a proportion. (base x height) divided by 2 on one side and 42 over 1 on the other.

`(2x(x-1))/(2)=(42)/(1)` Next, cross multiply. This involves taking the numerator of

one side (top) and multiplying it by the denominator

(bottom) of the other side.

84=2x(x-1) 42*2=84 and anything multiplied by 1 equals itself. Next,

distribute (multiply) the 2x by each term in the

parentheses.

84=2
`x^2`-2x 2x*x=2
`x^2`. 2x*-1=-2x. Next, subtract 84 from both sides.

0=2
`x^2`-2x-84 Now, you can simplify this by dividing by 2 on both sides.

0=
`x^2`-x-42 This is a quadratic equation, which means you have to

factor or use the quadratic formula. In this case, you can

factor by using product and sum. You have to find what

multiplies to -42 and adds to -1. Those numbers would be

-7 and 6. -7*6=-42 and -7+6=-1 Therefore, you will have

x-7 and x+6

0=(x-7)(x+6) Next, solve each equation with each binomial set equal

to 0. For x-7=0, x=7 because you add 7 to both sides. For

x+6=0, x=-6 because you subtract 6 from both sides.

x=7 x=-6

You can check if these values work by plugging them into the formula.

`(2x(x-1))/(2)- > (2*7(7-1))/(2)- > (14(6))/(2)- > (84)/(2)- > 42`. x can be 7.

`(2x(x-1))/(2)- > (2*-6(-6-1))/(2)- > (-12(-7))/(2)- > (84)/(2)- > 42` x can be -6

The base and height are the numbers in the numerator of the equation after the 3rd arrow for both processes.

Answer 2

Height: 6

Base: 14

Explanation:

Area=42 in^2

height=x-1

base=2x

bh/2=42

Substitute in the values:

2x(x-1)/2=42

The 2s cancel out each other.

x(x-1)=42

x^2 - x =42

x^2 - x - 42=0

When we factor that, we get:

(x-7)(x+6)=0

x=7 or x=-6

We will take the positive answer.

height= x-1 = 7-1 = 6

base= 2x = 2(7) = 14

Now let's double check if we are correct.

6(14)/2

=84/2

=42

We are correct!