Question

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

A) right
B) acute
C) obtuse
D) none of the above
A triangle has side lengths 44, 36 and 30. What type of triangle is it?
A) right
B) acute
C) obtuse
D) none of the above

Answer 1

Part A) Option C. obtuse

Part B) Option B. acute

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)<a^(2)+b^(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