Question

Which value of x would make SUV TUW by HL?

Answer 1

Answer: The value of x must be 5 units to make ΔSUV ≅ ΔTUW by HL.

Explanation:

Since we have given the following figure:

Consider, ΔSUV and ΔTUW,

We need to make it ΔSUV ≅ ΔTUW

Since we have given that

∠SUV = ∠WUT=90° (Vertically opposite angles are equal too)

UV = UW (Given)

and SV must be equal to WT to make it congruent triangles.

So, SV = WT

`2x+9=4x-1\\\\9+1=4x-2x\\\\10=2x\\\\x=(10)/(2)=5\ units`

Hence, the value of x must be 5 units to make ΔSUV ≅ ΔTUW by HL.

Answer 2

In the HL theorem, the hypotenuse and one length of the two triangles are equivalent. In order to calculate the value of x, we equate the two values of the hypotenuse:
2x + 9 = 4x - 1
2x = 10
x = 5

With x = 5, the hypotenuse of SUV works out to be 19, and the hypotenuse of WUT also works out to be 19.