Question

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?

Answer 1

Base:12 Height=5

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

Answer 2

Base 12m Height 5m

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