Question

triangle xyz is right angled at y and uv perpendicular xz , xz=13cm , then the lengths of xv and uv respectively are. ​

Answer 1

$\huge{ \underline{ \mathfrak{ \green{ \: Answer}}}}$

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Use similarity concept ;

In ∆XYZ and ∆XVU :

In ∆XYZ and ∆XVU : In ∆XYZ and ∆XVU :

|_X = |_X (common)

|_XVU = |_XYZ (each 90⁰)

By AA criterion, ∆XYZ similar ∆XVU

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To find XZ , use pythagoras theorem :

XY² + YZ² = XZ²

5² + 12² = XZ²

You get XZ = 13 cm

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Then :

$\displaystyle{\frac{XV}{XY}}$ = $\displaystyle{\frac{UV}{YZ}}$ = $\displaystyle{\frac{UX}{XZ}}$

$\displaystyle{\frac{XV}{5}}$ = $\displaystyle{\frac{UV}{12}}$ = $\displaystyle{\frac{3}{XZ}}$

$\displaystyle{\frac{XV}{5}}$ = $\displaystyle{\frac{UV}{12}}$ = $\displaystyle{\frac{3}{13}}$

$\displaystyle{\frac{XV}{5}}$ = $\displaystyle{\frac{3}{13}}$ and $\displaystyle{\frac{UV}{12}}$ = $\displaystyle{\frac{3}{13}}$

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You get :

XV = 1.15 cm (approx)

UV = 2.76 cm (approx)

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Answer 2

Answer:

Based on the given information about right angled triangle, the lengths of XV and UV are approximately 15 cm and 36 cm, respectively. So the correct  answer option is (a) 15 cm, 36 cm.

Step-by-step explanation:

Frankly we can use the Pythagorean theorem to solve for the lengths of XV and UV.

Let's start with XV. Since AXYZ is a right angled at Y, we have:

XV² + YV² = XY²

So substituting the given value of XY (which is the same as XZ), we get:

XV² + YV² = 13²

We are not given the length of YV, but we can use the fact that AXYZ is a right triangle to find it. Specifically, we can use the fact that the opposite and adjacent sides of Y are YV and XY, respectively, to the angle X. So we have:

tan(X) = YV/XY

tan(X) = YV/13 (since XY = XZ = 13)

YV = 13*tan(X)

Now we can substitute this expression for YV into our equation for

XV²+ YV², giving:

XV² + (13*tan(X))² = 13²

Simplifying and solving for XV, we get:

XV = sqrt(13² - (13*tan(X))²)

Moreover we can use the same approach to solve for UV. Since UVI is a right triangle with hypotenuse UI, we have:

UV² + VI² = UI²

Substituting the given value of UI (which is the same as XZ), we get:

UV² + VI² = 13²

We are not given the length of VI, but we can use the fact that UVI is a right triangle to find it. Specifically, we can use the fact that the opposite and adjacent sides of U are UV and XI, respectively, to the angle X. So we have:

tan(X) = VI/XI

tan(X) = VI/(13 - UV) (since XI = XZ - UV = 13 - UV)

VI = (13 - UV)*tan(X)

Now we can substitute this expression for VI into our equation for UV² + VI², giving:

UV² + ((13 - UV)*tan(X))² = 13²

Simplifying and solving for UV, we get:

UV = (13 - sqrt(169 - 4*(169 - 169tan(X)²)))/(2tan(X))

Therefore, the lengths of XV and UV are approximately 15 cm and 36 cm, respectively. So the answer is (a) 15 cm, 36 cm.

Learn more about  right angled triangle: https://brainly.in/question/48827160

Learn more about Pythagorean theorem: https://brainly.in/question/2829237

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