Question

The length of one side of a right triangle is shown in this diagram.What could be the lengths of the two remaining sides of the triangle?A. 6 inches and 12 inchesB. 10 inches and 12 inchesC.15 inches and 17 inchesD. 16 inches and 25 inches

Answer 1

Step 1

Given; The length of one side of a right triangle is shown in this diagram.

What could be the lengths of the two remaining sides of the triangle?

Step 2

Euclidean geometry, For a right-angled triangle, the sum of the square of the two shorter sides of a right triangle is equal to the third side, which is the longest; in symbols,

`a^2=b^2+c^2`

From the image; Using the Pythagoras theorem we have that

`\begin{gathered} a^2-b^2=8^2 \\ where\text{ a=longest side or hypotenuse} \\ b=other\text{ unknown side} \end{gathered}`
`\begin{gathered} Checking\text{ the options;} \\ 17^2-15^2=64 \end{gathered}`
`64=8^2`

Thus the answer is;

`15\text{ inches and 17inches}`