Question

1. is triangle mno a right triangle? explain.

n (37 cm)---o
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m (35 cm)---o (12 cm)

Explanation:

Step1: Recall Pythagorean theorem

For a triangle to be right - angled, the sum of the squares of the two shorter sides should equal the square of the longest side. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse (longest side) and $a,b$ are the other two sides.
Here, the side lengths are 12 cm, 35 cm, and 37 cm. The two shorter sides are 12 cm and 35 cm, and the longest side is 37 cm.

Step2: Calculate the square of each side

• Calculate $12^{2}$: $12^{2}=12\times12 = 144$
• Calculate $35^{2}$: $35^{2}=35\times35=1225$
• Calculate $37^{2}$: $37^{2}=37\times37 = 1369$

Step3: Check Pythagorean theorem

Add the squares of the two shorter sides: $12^{2}+35^{2}=144 + 1225=1369$
And we see that $12^{2}+35^{2}=37^{2}$

Answer:

Yes, triangle MNO is a right triangle. Because when we check the Pythagorean theorem for the side lengths 12 cm, 35 cm, and 37 cm, we find that $12^{2}+35^{2}=37^{2}$ (since $144 + 1225 = 1369$ and $37^{2}=1369$), which satisfies the Pythagorean theorem for a right - triangle.