Question

How do you translate “ten less than five times the area of a triangle” into an algebraic expression?

Answer 1

Hint: To solve the above question we need to translate the given words into the algebraic expression. An algebraic expression in mathematics is an expression which is made up of variables and constants with algebraic operation like addition, subtraction, multiplication, and division.

Complete step by step solution:
Let's suppose the area of the triangle is A. we know the area of the triangle is:$A=\dfrac{1}{2}\left( base\times height \right)$. In the above question “less than” means subtraction and “more than” will always mean addition. We will translate the words of the given question into algebraic equations in small pieces and then we will combine them.
Now the first part of the above equation says “ten less than five times the area of the triangle”, it means this part is going to be subtracted from the rest of the equation. 5 times the area of triangle looks like in the equation form as:
$\Rightarrow 5\left( \dfrac{1}{2}\left( b\times h \right) \right)$, Where $b$ is the base of the triangle and $h$ is the height of the triangle.
So we have solved the half part of the given question. Now It is written in the question “ten less than the five times the area of a triangle” then we get,
$\Rightarrow \dfrac{5}{2}bh-10$
Hence we get the final algebraic expression $\dfrac{5}{2}bh-10$.

Note: To solve these types of questions we should know the meaning of some simple words like less than which means minus, added to which means addition, and product, of means multiplication. Here we can be wrong by subtracting the $\dfrac{5}{2}bh$ from 10, so always read words carefully and interpret them correctly.