Triangles s u v and r u w are connected at point u. angles s u v and w u t are right angles. the length of hypotenuse s v is 2 x + 9 and the length of hypotenuse w t is 4 x minus 1. sides v u and u w are congruent. which value of x would make triangle s u v is-congruent-to triangle t u m by hl? 2 3 4 5

Option D. x = 5

Step-by-step explanation:

Figure for the given question is not attached; please find the figure attached with the answer.

In this figure, ∠SUV ≅ ∠WUT ≅ 90°

Length of hypotenuse SV = 2x + 9

and length of hypotenuse WT = 4x - 1

Sides VU ≅ UW

If triangles SUV and TUM are congruent, by the property of (HL) Hypotenuse-Leg theorem

VU ≅ UW  [Given]

Hypotenuse SV ≅ TW

2x + 9 = 4x - 1

4x - 2x = 9 + 1

2x = 10

x =

x = 5

Therefore, option D. x = 5 is the answer.

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step-by-step explanation: