Question

Draw an equilateral triangle whose side is

5 \sqrt{2} cm

. Draw a parallelogram whose area is double the area of the equilateral triangle on the same base with one angle as

30 °

.

Accepted Answer

We have to draw an equilateral triangle of side $5 \sqrt{2} cm$ . On the same base and same area we have to draw a parallelogram whose one angle is $30 °$ .

Area of parallelogram $= 2 \times$ Area of equilateral triangle

Area of equilateral triangle $= \frac{\sqrt{3}}{4} \times a^{2} = \frac{\sqrt{3}}{4} \times 5 \sqrt{2} \times 5 \sqrt{2} = \frac{25 \times 2 \times \sqrt{3}}{4} = \frac{25 \sqrt{3}}{2}$

Area of parallelogram $= b \times h$

$\Rightarrow 5 \sqrt{2} \times h = 2 \times \frac{25 \sqrt{3}}{2} \Rightarrow h = \frac{5 \sqrt{3}}{\sqrt{2}} = 6.1 c m$

Steps for construction:

Draw the base $A B$ of length $5 \sqrt{2} c m$ .

Now taking end points make arc from both the end points.

The point of intersection of both the arcs is termed as $C$ which is the third vertex of the triangle.

Now to draw the parallelogram bisect the angle $∠ C A B$ forming an angle of $∠ X A B = 30 °$ .

Now construct an angle of $150 ° ∠ A B Y$ .

Cut an arc from both sides of length $6.1 c m$ .

Join the end point $D$ and $E$ to form parallelogram $A B E D$ of area equal to the triangle $△ A B C$ .

Draw an equilateral triangle whose side is $5 \sqrt{2} cm$ . Draw a parallelogram whose area is double the area of the equilateral triangle on the same base with one angle as $30 °$ .

Important Questions on Miscellaneous Exercise : Geometry

Learn and Prepare for any exam you want !

Draw an equilateral triangle whose side is 52 cm. Draw a parallelogram whose area is double the area of the equilateral triangle on the same base with one angle as 30°.

Important Questions on Miscellaneous Exercise : Geometry

Learn and Prepare for any exam you want !

Draw an equilateral triangle whose side is $5 \sqrt{2} cm$ . Draw a parallelogram whose area is double the area of the equilateral triangle on the same base with one angle as $30 °$ .