Answer:
(a) {6, 8, 10} cm
(b) {12, 35, 37} cm
(d) {10, 24, 26} cm
Explanation:
You want to know which of the given sets of dimensions could be those of a right triangle.
- 6, 8, 10 cm
- 12, 35, 37 cm
- 4, 6, 10 cm
- 10, 24, 26 cm
Pythagorean theorem
A set of side lengths will form a right triangle if they satisfy the Pythagorean theorem:
a² +b² = c²
Application
6² +8² = 36 +64 = 100 = 10² . . . . . {6, 8, 10} forms a right triangle
12² +35² = 144 +1225 = 1369 = 37² . . . . . {12, 35, 37} forms a right triangle
4 + 6 = 10 . . . . . {4, 6, 10} doesn't even form a triangle
10² +24² = 100 +576 = 676 = 26² . . . . . {10, 24, 26} forms a right triangle
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Additional comment
For three side lengths to form a triangle, the sum of the two short sides needs to be longer than the longest side. (This is the triangle inequality.)
Lengths 4, 6, 10 do not meet that requirement.
You may notice that the long sides of these triangles differ in length by 2 units. The short side is twice the square root of their average. This relation will hold for any right triangles having long sides that differ by 2.
{6, 8, 10} ⇒ 6 = 2·√9
{12, 35, 37} ⇒ 12 = 2·√36
{10, 24, 26} ⇒ 10 = 2·√25
Along the same lines, if the longest sides differ by 1, the short side is the square root of their sum.