Respuesta :

Answer:

ST = 12.2

Step-by-step explanation:

See the attached diagram of the triangle.

Here, Δ RST, Δ RSV and Δ STV all are right triangles.

If we assume that, ST = x and SR = y, then

From Δ RSV and Δ STV we get,

SV² = RS² - RV² = ST² - VT²

⇒ y² - 4.2² = x² - 10.3²

⇒ x² - y² = 88.45 .......... (1)

Now, from Δ RST, we have

ST² + SR² = RT²

⇒ x² + y² = (10.3 + 4.2)² = 210.25 .............. (2)

Now, adding equations (1) and (2) we get,

2x² = 298.7

⇒ x² = 149.35

⇒ x = 12.2 (Rounded to the nearest tenth}

So, ST = 12.2 (Answer)

Ver imagen rani01654

The length of ST is 12.22.

Given that

In the right triangle RST below, altitude SV is drawn to hypotenuse RT.

If RV=4.2 and TV = 10.3.

We have to determine

What is the length of ST?

According to the question

Let the length of ST be x;

In the right triangle RST below, altitude SV is drawn to hypotenuse RT.

If RV=4.2 and TV = 10.3.

The length of the ST is determined by using the Pythagoras theorem.

[tex]\rm Hypotenuse^2 = Base^2+ Perpendicular ^2[/tex]

In the Δ RSV and Δ STV;

[tex]\rm Sv^2 = RS^2- RV^2= ST^2 - VT^2\\\\ y^2 - 4.2^2 = x^2- 10.3^2\\\\x^2 - y^2 = 88.45 [/tex]

Again in Δ RST;

[tex]\rm ST^2 + SR^2 = RT^2\\\\\ x^2+ y^2= (10.3 + 4.2)^2\\ \\ x^2+ y^2= 210.25 [/tex]

On adding both the equations;

[tex]\rm x^2+y^2+x^2-y^2= 88.45+210.25\\ \\ 2x^2= 298.7\\ \\ x^2 = \dfrac{298.7}{2}\\ \\ x^2 = 149.35\\ \\ x = 12.22[/tex]

Hence, the length of ST is 12.22.

To know more about Triangles click the link given below.

https://brainly.com/question/25813512

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