Q20. - Algebra 1

Question

PERIEAETER Find the value of x so that the triangles have the same perimeter. (Lesson 2-4)

Step-by-Step Solution

Answer

$x=20$

Step 1. Given information.

Sides of first triangle: $x-5,x-4\text{ and }5$.

Sides of second triangle: $x-10,10\text{ and }16$

And given that perimeter of both triangles are same.

Step 2. Perimeter of a triangle.

The perimeter of a triangle is the sum of its three sides.

Step 3. Description of step.

Since if the perimeter of both the triangles be same, thus the value of x can be find by using the formula for perimeter of triangle and equation perimeter of both triangles, as:

$\left(x-5\right)+\left(x-4\right)+5=\left(x-10\right)+10+16$

Step 4. Calculation.

Now finding the value of x as,

$$\begin{gathered} \left(x-5\right)+\left(x-4\right)+5=\left(x-10\right)+10+16 \\ x-5+x-4+5=x-10+26 \\ 2x-4=x+16 \\ 2x-x=16+4 \\ \Rightarrow x=20 \end{gathered}$$

Thus, value of x is 20.