A base of a triangle is two more than four times its height. If the area of the triangle is 595 square inches, find its base and height. (If needed, round answers to 5 decimal places.)

Question

Can I get some help with this problem? Thanks in advance for the help!

Answer 1

Hi Anthony W.

Since we are given the following;

base = (4*(height) + 2)

595 = Area

For a Triangle we know or we can look up

A = 1/2(b*h)

OR

A =bh/2

Where

A = Area

b = base

h = height

We can make the following substitutions

A = bh/2

595 = (4h+ 2)*h/2

Remove the parentheses

595 = 4h² + 2h/2

Multiply both sides by 2

1190 = 4h² + 2h

Subtract 1190 from both sides

0 = 4h² + 2h - 1190

We have a quadratic that can be factored

4h² + 2h - 1190 = 0

(2h - 34)(2h + 35) = 0

Since we are talking about a length only the positive result is applicable

Can you solve for h, the height and use the positive result to find the base?

Please give it a try

If you have any questions send me an email.