Question

Given that line m perpendicular bi sector of EF and EH=100 find EF?

Answer 1

The length of the sides would be as follows:

1. EF is 100 units.

2. GH is
`\(√(269)\)` units.

1. **Perpendicular Bisector and EH = 100:**

Given that line m is the perpendicular bisector of segment FH, we can infer that EH is the perpendicular distance from point E to line m. If EH is given as 100 units, we can use this information to find EF.

Since line m is the perpendicular bisector, it divides FH into two equal halves. Therefore, EF is also equal to FH. Hence, EF = FH = 100 units.

2. **Given EF = 13, FH = 10, and EH = 13:**

We can use the triangle inequality theorem to check if the given side lengths form a valid triangle. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, EF + FH = 13 + 10 = 23, which is greater than EH (13). Therefore, the given side lengths form a valid triangle.

Now, to find GH, we can use the Pythagorean theorem since GH is the hypotenuse of the right-angled triangle EGH:

`\[GH = √(EF^2 + FH^2) = √(13^2 + 10^2) = √(169 + 100) = √(269).\]`

So, GH is equal to the square root of 269 units.

The probable question may be:

Given that line m is the perpendicular bisector of F FH and EH=100 , find EF. m 2.Given that EF=13 FH=10 , and EH=13 , find GH.