Answer:
Question 6 & 9 is not a right-angled triangle. However, Question 7 & 8 is right-angled triangle.
Explanation:
A triangle can be determined to be a right-angled triangle if and only if one of the following conditions is satisfied:
Pythagorean Theorem: If in a triangle, the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right-angled triangle. Symbolically, if a, b, and c are the lengths of the sides of the triangle, with c being the length of the hypotenuse, then a^2 + b^2 = c^2.
Angle criterion: If in a triangle, one of the angles is equal to 90 degrees, then the triangle is a right-angled triangle.
Right Angle Mark: If a triangle has a right angle mark (a small square) on one of its angles, then it is a right-angled triangle.
By using any one of the above methods, you can determine whether a triangle is a right-angled triangle or not.
So, Question no 6
Let the distance between three cities be a, b and c i.e. 45 miles, 56 miles and 72 miles.
using Pythagoras theorem,
a^2 + b^2 = c^2
45^2+56^2=72^2
2025+3136=5184
5161=5184
Hence, It's not a right-angled triangle.
So, Question no 7 has three sides a, b and c i.e. 4 ft, 3 ft and 5 ft.
using Pythagoras theorem,
a^2 + b^2 = c^2
4^2+3^2=5^2
16+9=25
25=25
Hence, it's a right-angled triangle.
Question no 8 also have three sides a, b and c i.e. 5 in, 12 in and 13 in.
using Pythagoras theorem,
a^2 + b^2 = c^2
5^2+12^2=13^2
25+144=169
169=169
Hence, it's a right-angled triangle.
Question no 9 also have three sides a, b and c i.e. 9.5 feet, 16 feet and 18.5 feet.
using Pythagoras theorem,
a^2 + b^2 = c^2
9.5^2+16^2=18.5^2
90.25+256=342.25
346.25=342.25
Hence, It's not a right-angled triangle.