The statement "the square of the longest side is equal to the sum of the squares of the two shorter sides" is true for a right-angled triangle.
(a) 5 cm, 12 cm and 13 cm
The statement is represented as:
[tex]\mathbf{13^2 = 12^2 + 5^2}[/tex]
[tex]\mathbf{169= 144 + 25}[/tex]
[tex]\mathbf{169= 169}[/tex]
Hence, the statement is true for triangle (A)
(b) 4 cm, 5 cm and 7 cm
The statement is represented as:
[tex]\mathbf{7^2 = 5^2 + 4^2}[/tex]
[tex]\mathbf{49 = 25 + 16}[/tex]
[tex]\mathbf{49 = 41}[/tex]
Hence, the statement is not true for triangle (B)
(c) 3 cm, 4 cm and 5 cm
The statement is represented as:
[tex]\mathbf{5^2 = 4^2 + 3^2}[/tex]
[tex]\mathbf{25 = 16 + 9}[/tex]
[tex]\mathbf{25 = 25}[/tex]
Hence, the statement is true for triangle (C)
(d) 9 cm, 12 cm and 15 cm
The statement is represented as:
[tex]\mathbf{15^2 = 12^2 + 9^2}[/tex]
[tex]\mathbf{225 = 144 + 81}[/tex]
[tex]\mathbf{225 = 225}[/tex]
Hence, the statement is true for triangle (D)
Read more about triangles at:
https://brainly.com/question/19182121
