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

Question

3 years ago

8

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

Mathematics

2 answers:

azamat · Answer 1 · 2022-05-29T03:46:48+03:00

azamat3 years ago

3 0

<h2>THE ANSWER IS D. 5</h2>

my answer is too short so just ignore this part but I can promise the answer is five.

padilas [110] · Answer 2 · 2022-05-29T06:09:21+03:00

Answer:

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 = $\frac{10}{2}$

x = 5

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