Exercise 25 Page P3

To find the missing side length of the triangle, we will use the Pythagorean Theorem. a^2+b^2=c^2In the formula, a and b are the legs and c is the hypotenuse of a right triangle. We are given a triangle with a=20cm and b=21cm.

Let's substitute these values into the formula.

a^2+b^2=c^2

SubstituteII

a= 20, b= 21

20^2+ 21^2=c^2

▼

Solve for c

CalcPow

Calculate power

400+441=c^2

AddTerms

Add terms

841=c^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(841)=c

RearrangeEqn

Rearrange equation

c=sqrt(841)

CalcRoot

Calculate root

c=29

Since a negative side length does not make sense, we only need to consider positive solutions.

Checking Our Answer

Let's Check!

We can check our answer by substituting the missing length that we found, which is the hypotenuse in this case, back into the equation. When we simplify both sides, they should be equal.

a^2+b^2=c^2

SubstituteValues

Substitute values

20^2+ 21^2? = 29^2

CalcPow

Calculate power

400+441? =841

AddTerms

Add terms

841=841 ✓

Extra

Pythagorean Triples

Another way that we can sometimes find a missing side length of a right triangle is by understanding and recognizing when the measurements create a Pythagorean Triple.

Pythagorean Triple
A set of three natural numbers that satisfies the Pythagorean Theorem.

The first few Pythagorean triples are shown in the table below.

Pythagorean Triples
Triple	Pythagorean Theorem
3, 4, 5	3^2+ 4^2= 5^2
7, 24, 25	7^2+ 24^2= 25^2
5, 12, 13	5^2+ 12^2= 13^2
20, 21, 29	20^2+ 21^2= 29^2

Hints

Check the answer

Checking Our Answer

Extra