The height of a triangle is 7 m less than its base. The area of the triangle is 30 m².

What is the length of the base? What is the height of the triangle?

Base 12m Height 5m

Step-by-step explanation:

Area of a triangle formula A=1/2bh

30=1/2 (x) (x-7)

2*30 = 1/2 (x) (x-7) * 2

60 = x^2 - 7x

60 - x^2 + 7x = 0

-60 + x^2 - 7x = 0

x^2 - 7x - 60 = 0

x^2 + 5x - 12x - 60 = 0

x (x+5) - 12x-60=0

x (x+5) - 12 (x+5) = 0

(x+5) * (x-12) = 0

x+5=0

x-12=0

x=-5

x-12=0

x=12

The final answer is: x = 12,5

get rid of the - 5 because - 5 does not make sense at a height so turn it into 5

Base: 12m

Height 5m

Base:12 Height=5

Step-by-step explanation:

Step 1

Know the formula your using to solve this problem

A=/frac{1}{2} / / BH

Step 2

Now you look at what you already know

A=/frac{1}{2} / / B (+7) H (-7)

Step 3

Divide 30 by 1/2

In order to do this you convert / frac{1}{2} / into a decimal which is 0.5

so now divide 30 by 0.5 which Equals

60

Step 4

Now Multiply all the numbers that equal 60 until finding a solution where one number is 7 less then the number it's being multiplied by

Solution=12 * 5=60

Step 5

Now you that you have you solution you plug this into the formula to find the area

A=/frac{1}{2} / B (12) H (5) note: It is easier to write 0.5 in place of / frac{1}{2} / because it will make it easier for you to solve this problem.

Step 6

Now you have everything needed to solve

A=0.5 * 60

A=30m² Base=12 Height = 5