Question

IT IS DUE AT 11:59PM. PLEASE HELP!!!!

The height of a triangle is 7 inches less than 5 times the length of its base. The area is 26 square inches. Find the length of the base and the height of the triangle.

Answer 1

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 2

Height: 13 Base: 4

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