Question

The base of a triangle is given by a number, x (metres). The height of the triangle is ten metres less than the product of two and the number. The area of the triangle is equal to the product of seven and the base length.

Answer 1

According to the question the base of the triangle is x, the height is ten less than the product of two and x, this is 2x-10. The area of the triangle is the product of seven and the base, this is 7x.

The area of a triangle is given by:

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

Replace each variable for the given expressions:

`\begin{gathered} 7x=(x\cdot(2x-10))/(2) \\ 7x=(2x^2-10x)/(2) \\ 7x=x^2-5x \\ 7=x-5 \\ x=7+5 \\ x=12 \end{gathered}`

x has a value of 12.