Which value of x would make SUV TUW by HL?

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.

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RenatoMattice RenatoMattice · Answer 2 · 2019-02-13T10:31:38+01:00

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

Step-by-step 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

[tex]2x+9=4x-1\\\\9+1=4x-2x\\\\10=2x\\\\x=\frac{10}{2}=5\ units[/tex]

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