Question

8.4 Could be the Hypotenuse, Could be a
Leg
PLSSSSSSSSS HELPPPPPPPPPPPP

Answer 1

1. x = 5

2. x =
`\sqrt 7 \approx` 2.65

Explanation:

To solve these problems, we can use the diagram below, as well as Pythagoras's Theorem, which states:

`\boxed{\mathrm{a^2 = b^2 + c^2}}`,

where a is the hypotenuse (longest side) of a right-angled triangle, and b and c are the legs of the triangle.

1. x is the hypotenuse:

From the diagram below, we can see that, if x is the hypotenuse of the triangle, then 3 and four are the legs of the triangle. Therefore, using the above equation:

`x^2 = 3^2 + 4^2`

⇒
`x = √(3^2 + 4^2)` [Taking the square root of both sides of the equation]

⇒
`x = √(25)`

⇒
`x = \bf 5`

2. x is one of the legs:

From the diagram below, we can see that when x is one of the legs, the hypotenuse is 4, and the other leg is 3.

The hypotenuse isn't 3 because the hypotenuse is the longest side in a right-angled triangle, and 4 is longer than 3.

Therefore,

`4^2 = x^2 + 3^2`

⇒
`x^2 = 4^2 - 3^2` [Subtracting 3² from both sides]

⇒
`x = √(4^2 - 3^2)` [Taking the square root of both sides of the equation]

⇒
`x = √(7)`

`\approx \bf 2.65`