Question

please explain how to solve this I need help urgently! I already have the answer, I just don't know the steps to solve!​

Answer 1

You are given area which is equal to 115 and the dimensions base which is equal 5x-2 and the height 2x. You know mathematically that the formula to calculate the area of a triangle is

`a= (1)/(2) * b * h`

PLUG IN THE DIMENSIONS OF THE BASE AND HEIGHT TOGETHER WITH THE AREA GIVEN

`115 = (1)/(2) * (5x - 2)(2x) \\ 230 = (5x - 2)(2x) \\ 230 = 10 {x}^(2) - 4x \\ 10 {x}^(2) - 4x - 230 = 0 \\ 2(5 {x }^(2) - 2x - 115) = 0 \\ 5 {x }^(2) - 2x - 115 = 0 \\`

USING THE QUADRATIC FORMULA

`x = \frac{ - b (+ - ) \sqrt{ {b}^(2) - 4ac} }{2a} \\ \\ x = - 4.6 \: or \\ x = 5 \\ \\ \\`

now I found out that x will never be equal to -4.6 because when I substitute it to 2x to get the height it gived me a negative number.

This brings us to a conclusion that x =5

to get the constant valuez of the dimensions Plug in x

b= 5(5)-2

base=25-2

base=23

height=2(5)

height=10

keep in mind distance will never be negative!!!!!!!! that is why -4.6 was excluded as the solution.

I hope this helps.