Question

Construct a right angle triangle XYZ in which angle Z = 90°, YZ= 3cm , XZ+XY= 5cm​

Answer 1

Step-by-step explanation:

don't know guys but tried my best

Answer 2

Step-by-step explanation:

$\triangle XYZ$ is a right-angled triangle where $\angle Z=90 ^\circ$

$YZ = 3 cm$    (given)

$XZ+XY = 5 cm$     (given)      —(i)

So, $XY$ is the hypotenuse   (opp.side of a right angled triangle)

By pythagoras theorem,

$(XY)^2 = (XZ)^2 + (YZ)^2\\(XY)^2 - (XZ)^2 = (YZ)^2$

$(XY+XZ)(XY-XZ) = (3)^2$    [Since $a^2 - b^2 = (a+b)(a-b)$]

$5(XY-YZ) = 9 cm\\XY-XZ = \frac{9}{5} cm$         —(ii)

Solving (i) and (ii), we get

$XY + XZ = 5\\XY - XZ = 5\\2XY = 5 cm + \frac{9}{5} cm\\XY = 3.4 cm\\XZ = 1.6 cm$

Now, as we have the values so we can construct the  $\triangle XYZ$ using these instructions :

Draw a line $YX$ of $3 cm$.

Draw an angle of $90^\circ$ at $Z$ and extend the line.

Take a measure of $1.6 cm$ on your compass and cut an arc at the extended line by keeping the compass needle at $Z$. We will get point $X$.

Join $XY$.

We have got the required triangle as in the figure.