Write the equation that correctly shows the area of the triangle in terms of its height, h. PLEASE HELP!

Question

A carpenter is building a set of trusses to support the roof of a residential home. In the blueprints, she has determined that she needs to make a support triangle with an area 56m2 . She knows that the base must be 1 less than 2 times the height. Write the equation that correctly shows the area of the triangle in terms of its height, h.

Answer 1

This looks like a quadratic formula problem.

First, let's set ourselves up: Area of Triangle is A = 1/2 bh

Area = 56 m²

Base = 2h - 1 <---------- from your problem, base is "1 less than 2 times the height" so that is 2h - 1

Substitute 2h-1 for b and 56 for A.

56 = 1/2 (2h-1)h <-------------- let's multiply both sides by 2 to get rid of the 1/2

112 = (2h-1)h <-------------- let's multply the right side of the equation

112 = 2h² - h <-------------- let's subtract 112 from both sides so that we have a quadratic equal to 0

0 = 2h² - h - 112

Try to find two factors that multiply to (2)(-112) = -224 and add up to -1. Not possible! So we must use the quadratic formula.

a = 2 , b = -1, c = -112 [plug these in for your own work]

We use h instead of x, and get:

h = 1 + sqrt(897) = 7.737 or h = 1 - sqrt(897) = -7.237

4 4

Since height cannot be negative, we must use h = 7.737.

Final answer: h = 7.737 meters.