Question

A triangle has side lengths 32, 45 and 18. What type of triangle is it?

Answer 1

Answer:

Part A) Option C. obtuse

Part B) Option B. acute

Step-by-step explanation:

we know that

Applying the Pythagoras Theorem

if $c^{2}=a^{2}+b^{2}$ ----> is a right triangle

if $c^{2}>a^{2}+b^{2}$ ----> is an obtuse triangle

if $c^{2}$ ----> is an acute triangle  

where

c is the greater side

Part A) A triangle has side lengths 32, 45 and 18. What type of triangle is it?

we have

$c^{2}=45^{2}=2,025$

$a^{2}+b^{2}=32^{2}+18^{2}=1,348$

therefore

$c^{2}>a^{2}+b^{2}$

Is an obtuse triangle

Part B) A triangle has side lengths 44, 36 and 30. What type of triangle is it?

we have

$c^{2}=44^{2}=1,936$

$a^{2}+b^{2}=36^{2}+30^{2}=2,196$

therefore

$c^{2}< a^{2}+b^{2}$

Is an acute triangle