Question

this figure shows a right angle triangle ABC with Dimensions as shown. (i) Given that the perimeter of the triangle is 17cm, write down an expression, in terms of X, for the length of AB(ii) write down an equation in X represent the information and show that is simplified 2x^2-18x+17=0(iii) solve the equation 2x squared - 18x + 17 = 0 (iv) hence, find the area of the triangle

Answer 1

Part i)

The perimeter is the sum of the measures of all the sides of a geometric figure.

Then, we can write the following equation:

`\begin{gathered} \text{ Perimeter }=AB+BC+AC \\ \text{ We replace the known values} \\ 17=AB+x+8 \end{gathered}`

Now, we can solve the above equation for AB:

`\begin{gathered} \text{ Subtract x and subtract 8 from both sides of the equation} \\ 17-x-8=AB+x+8-x-8 \\ 17-x-8=AB \end{gathered}`

Therefore, the expression, in terms of x, for the length of AB is:

`AB=17-x-8`

Part ii)