We want to find out if a hypotenuse of a photograph we cut into a right triangle is a rational number. To do so, we will use the Pythagorean Theorem and then classify the value we will find. Let's begin by recalling the Pythagorean Theorem.
a^2+ b^2= c^2
In this formula, a and b are the lengths of the legs, and c is the length of the hypotenuse of a right triangle. From the exercise, we know that the lengths of the legs of the triangle are 4 inches and 6 inches. We will substitute these values into the formula and solve it for c. Let's do it!
The length of the hypotenuse is sqrt(52). Next, we will recall how we can classify real numbers.
From the graph, we can see that real numbers are formed by two sets, rational and irrational numbers. Recall that we cannot write an irrational number as a fraction ab, where a and b are integers and b ≠0. Let's take a look at a table with some examples of irrational numbers.
A number which decimal form neither terminates nor repeats.
1.267662 ..., 0.675634 ...
Next, let's focus on the other set forming the real numbers, rational numbers. Rational numbers can be written as a fraction ab, where a and b are integers and b ≠0. Keeping this in mind, notice that 52 is not a perfect square. That means the length of the hypotenuse is not a rational number.
