Question

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

Answer 1

We are told that we want a triangle of area 56. Recall that the area of a triangle of base b and height h is given by the formula

`(b\cdot h)/(2)`

In our case we want

`(b\cdot h)/(2)=56`

now, we want to find an expression for b. We are told that the base is one less than twice the height. That is, we take the height, multiply it by 2, and then subtract 1. That would lead to

`b=2h\text{ -1}`

so we have

`\frac{h(2h\text{ -1\rparen}}{2}=56`

so the second option is correct.