Question

For each set of side lengths , classify the triangles based on whether it is a right triangle.

Answer 1

Answer:

(4,4, √32) and (8,7, √113) are the right angled triangles .

Step-by-step explanation:

A triangle is said to be right angled triangle if it satisfies the Pythagoras theorem.

Pythagoras theorem : $Hypotenuse^2=Perpendicular^2+Base^2$

A) 7,8,15

Hypotenuse = Largest side = 15

$Hypotenuse^2=Perpendicular^2+Base^2$

$15^2=7^2+8^2$

$225=49+64$

$225\neq 113$

So, It does not satisfy the Pythagoras theorem .

Hence it is not a right angled triangle.

B) 4,10,11

Hypotenuse = Largest side = 11

$Hypotenuse^2=Perpendicular^2+Base^2$

$11^2=10^2+4^2$

$121=100+16$

$121\neq 116$

So, It does not satisfy the Pythagoras theorem

Hence it is not a right angled triangle .

C) 4,4, √32

Hypotenuse = Largest side = √32

$Hypotenuse^2=Perpendicular^2+Base^2$

$(\sqrt{32})^2=4^2+4^2$

$32=16+16$

$32=32$

So, It satisfies the  Pythagoras theorem

Hence it is a right angled triangle .

D) 8,7, √113

Hypotenuse = Largest side = √113

$Hypotenuse^2=Perpendicular^2+Base^2$

$(\sqrt{113})^2=8^2+7^2$

$113=64+49$

$113=113$

So, It satisfies the  Pythagoras theorem

Hence it is a right angled triangle .

E) 4,4, √24

Hypotenuse = Largest side = √24

$Hypotenuse^2=Perpendicular^2+Base^2$

$(\sqrt{24})^2=4^2+4^2$

$24=16+16$

$24 \neq 32$

So, It does not satisfy the Pythagoras theorem

Hence it is not a right angled triangle .