Question

100 PTS solve for x ................

Answer 1

36.2

Explanation:

The tick marks on the two sides of the triangle indicate that the sides are of equal length. Therefore, as the triangle has two sides of equal length, it is an isosceles triangle.

In an isosceles triangle, the altitude is the perpendicular bisector of the base. Therefore, the triangle is made up of two congruent right triangles with:

• height = 33
• base = 30/2 = 15
• hypotenuse = x

To calculate the value of x, we can use Pythagoras Theorem:

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

where:

• a and b are the legs of the right triangle.
• c is the hypotenuse (longest side) of the right triangle.

Substitute the values into the formula and solve for x:

`\implies 15^2+33^2=x^2`

`\implies 225+1089=x^2`

`\implies 1314=x^2`

`\implies x^2=1314`

`\implies √(x^2)=√(1314)`

`\implies x=36.2491379...`

`\implies x=36.2\; \rm (nearest\;tenth)`

Therefore, the value of x is 36.2 units (nearest tenth).

Answer 2

x ≈ 36.2

Explanation:

the segment from the vertex of the triangle to the base is a perpendicular bisector, then

consider the right triangle on the right with legs 15 and 33 , hypotenuse x

using Pythagoras' identity in the right triangle

x² = 15² + 33² = 225 + 1089 = 1314 ( take square root of both sides )

x =
`√(1314)` ≈ 36.2 ( to the nearest tenth )