Question

Geo claims that the following sides of triangles 4 m, 7 m, 5 m, and 30 km, 122km, 125km. determine a right triangle. justify if his claims is TRUE.

Answer 1

Answer:

1) false

2) false

Step-by-step explanation:

apply pythagorous theorem

in both cases

7² is not equal to 5²+4²

there fore we can say it is not a right angled triangle

also

30² + 122² is not equal to 125²

there for we can say it is also not a right angled triangle

Answer 2

Concept:

Here we use the concept of the Pythagoras theorem.

Hypotenuse² = Perpendicular² + Base²

The longest side of a triangle is the hypotenuse.

Given:

The sides of the first triangle are 4m, 7m, and 5m.

The sides of the second triangle are 30km, 122km, and 125km.

Find:

Determine whether the given triangles are right-angle triangles.

Solution:

Apply Pythagoras theorem in the first triangle having sides 4m, 7m, and 5m.

Hypotenuse² = Perpendicular² + Base²               [Formula]

We know that the longest side is the hypotenuse

So, hypotenuse = 7m

Hypotenuse² = 7²

Hypotenuse² = 49

Now,

Perpendicular² + Base² = 4² + 5²

Perpendicular² + Base² = 16 + 25

Perpendicular² + Base² = 41

Hence, the triangle with sides of 4 m, 7 m, and 5 m is not a right-angle triangle. Since it does not satisfy Pythagoras's theorem.

Now, apply the Pythagoras theorem in the second triangle having sides of 30 km, 122km, and 125km.

Hypotenuse² = Perpendicular² + Base²               [Formula]

We know that the longest side is the hypotenuse

So, hypotenuse = 125km

Hypotenuse² = 125²

Hypotenuse² = 15625

Now,

Perpendicular² + Base² = 30² + 122²

Perpendicular² + Base² = 900 + 14884

Perpendicular² + Base² = 15784

Hence, the triangle with sides of 30 km, 122km, and 125km is not a right-angle triangle. Since it does not satisfy Pythagoras's theorem.

Hence, both the triangles do not satisfy the Pythagoras theorem. So, both are not right-angle triangles.

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