Question

2 Show that ◇LMN is isosceles if the median LD is perpendicular to the base MN.

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Answer 1

Answer:

LD will be common

MD=MN(LD is median)

angles are perpendicular

therefore LMD congurent LND

hence by CPCT LM =LN

and angle M = N

therefore by proving them congurent we can prove this

Answer 2

Step-by-step explanation:

Step-by-step explanation:

Step-by-step explanation:

Given :

Area of Trapezium is 384 cm² .

Parallel sides of trapezium are in the ratio 3:5 .

Perpendicular distance / Height is 12 cm .

To Find :

Length of each parallel sides .

Solution :

$\longmapsto\tt{Let\:one\:parallel\:side\:be=3x}$

$\longmapsto\tt{Let\:other\:parallel\:side\:be=5x}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}$

Putting Values :

$\longmapsto\tt{384=\dfrac{1}{{\cancel{2}}}\times{(3x+5x)}\times{{\cancel{12}}}}$

$\longmapsto\tt{384=(3x+5x)\times{6}}$

$\longmapsto\tt{384=18x+30x}$

$\longmapsto\tt{384=48\:x}$

$\longmapsto\tt{x=\cancel\dfrac{384}{48}}$

$\longmapsto\tt\bf{x=8}$

Value of x is 8 .

Therefore :

$\longmapsto\tt{Length\:of\:one\:parallel\:side=3(8)}$

$\longmapsto\tt\bf{24\:cm}$

$\longmapsto\tt{Length\:of\:other\:parallel\:side=5(8)}$

$\longmapsto\tt\bf{40\:cm}$

So , The Parallel sides of Trapezium are 24 cm and 40 cm .