Hello from MrBillDoesMath!
Answer: b = 4, h = 13
Discussion:
For a triangle with base b" and height "h, the area formula is
A= (1/2)bh.
In our case A = 26, h = 5b-7, so
26 = (1/2) b (5b-7). Multiply both sides by 2:
26*2 = b(5b-7) =>
52 = b(5b-7) =>
52 = 5b^2 - 7b => (subtract 52 from both sides)
5b^2 - 7b - 52 = 0. This factors as follows:
(b - 4) (5 b + 13) = 0 (use quadratic formula to find this)
so b = 4 and h = 5b -7 = 5*4 - 7 = 13
Thank you,
MrB
Answer:
Height: 13 Base: 4
Step-by-step explanation:
First, start by writing an equation.
[(5x-7)*x]/2=26
Because length *height /2 is area of triangle
Then just solve the equation
(5x-7)*x=52
5x^2-7x=52
Then,
5x^2-7x-52=0
Then you factor
(5x+13)(x-4)=0
So then 5x+13=0
5x=-13
x=-2.6
Not possible since negative number so try the other one
x-4=0
x=4
This is correct. You can also check your answer by adding it in.
[(5(4)-7)*(4)]/2=26
[(20-7)*4]/2=26
(13*4)/2=26
52/2=26
26=26
True, so correct.
Base:4
Height: 5*4-7
13
