Question

Construct a triangle $XYZ$ in which $\angle Y={30}^o$, $\angle Z={90}^o$ and $XY+ZX+YZ=11cm$.

Answer 1

Steps of Construction:

1. Draw a line segment $AB=11cm$. $(=PQ+QR+RP)$.

2. At $A$, construct an angle of ${30}^{\circ }$ and at $B$, an angle of ${90}^{\circ }$.

3. Bisect these angles. Let the bisectors of these angles intersect at a point $X$.

4. Draw perpendicular bisectors $ST$ of $AX$ and $UV$ of $BX$ .Let $ST$ intersect $AB$ at $Y$

5. Join $XY$ and $XZ$.

Then, $XYZ$ is the required triangle.