Question

A sail is in the shape of a right triangle. The area of the sail is 52 fr if the height is 5 feet greater than the base, find the base.

Answer 1

Since the triangle is a right triangle we can draw the triangle like so, calling x the distance corresponding to the base of the triangle and x+5 the height oh the triangle.

now use the formula of the area

`A=(bh)/(2)`

we now the area and the corresponding variables for the base and height, replace them on the formula

`52=(x\cdot(x+5))/(2)`

clear for the x

`104=x^2+5x`

equal the equation to 0 and solve the quadratic equation or by factorization

`x^2+5x-104=0`
`(x-8)\cdot(x+13)=0`

by factorization we know that roots are x=-13 and x=8, since we are talking about a distance the base of the triangle must be 8 ft.

check the answer with the formula of the area

`\begin{gathered} A=(bh)/(2) \\ A=(8\cdot(8+5))/(2) \\ A=(8\cdot13)/(2) \\ A=52 \\ 52=52 \end{gathered}`

The procedure is correct, the base of the triangle is 8 ft and the height is 13 ft.