Question

Can someone please help me answer this math question?

Answer 1

Answer:

x = 10

Step-by-step explanation:

The line from the vertex to the base is a perpendicular bisector.

Consider the left side right triangle, eith base = $\frac{1}{2}$ x

Using Pythagoras' identity.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

($\frac{1}{2}$ x )² + 7² = ($\sqrt{74}$ )², that is

$\frac{1}{4}$ x² + 49 = 74 ( subtract 49 from both sides )

$\frac{1}{4}$ x² = 25 ( multiply both sides by 4 to clear the fraction )

x² = 100 ( take the square root of both sides )

x = $\sqrt{100}$ = 10

Answer 2

Answer:

x = 10 units.

Step-by-step explanation:

The 2 triangles are congruent  by SAS.

Therefore the line of length x is bisected by the perpendicular line,

and they are both right triangles, so we can apply the Pythagoras theorem.

√74)^2 = 7^2 + (0.5x)^2

(0.5x)^2 =  74 - 49

0,25x^2 = 25

x^2 = 25/0.25

x^2 = 100

x = 10 (answer)