Chapter 1.5, Problem 75MR

To determine

The perimeter of an isosceles triangle with side lengths of $5+x,5+x,\text{ and }xy$ .

Answer to Problem 75MR

  $10+2x+xy$

Explanation of Solution

Given information:

The lengths of isosceles triangle as $5+x,5+x,\text{ and }xy$ .

Concept Used:

• Like terms are the terms that contain the same variable with similar exponents on it. Constants are like terms as well.

Distributive property:

• Left Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$
• Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

Perimeter of a geometric figure is the sum of all its sides. So, in order to find the perimeter of the given isosceles triangle, add all three sides of the triangle and simplify further as shown below,

  $\begin{array}{c}\text{Perimeter}=\left(5+x\right)+\left(5+x\right)+xy\\ =5+x+5+x+xy\\ =\left(5+5\right)+\left(x+x\right)+xy\\ =10+2x+xy\end{array}$

Thus, the perimeter of the given isosceles triangle is $10+2x+xy$ .