Question

the area of trapezium is 112 CM square its height 14 cm the larger parallel side is longer than other by 16 centimetre find the find the length of the parallel sides

Answer 1

Diagram:-

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• Height of a trapezium=14cm

Let

the shorter parallel side=x

The larger parallel side=x+16

• As we know that in a Trapezium

${\boxed{\sf Area={\dfrac {1}{2}}\times (sum\:of\:parallel\:sides)×height}}$

• Substitute the values

$\qquad\quad {:}\longmapsto\sf {\dfrac {1}{2}}(x+x+16)×14=112$

$\qquad\quad {:}\longmapsto\sf {\dfrac {1}{\cancel{2}}}(2x+16)×\cancel {14}=112$

$\qquad\quad {:}\longmapsto\sf 7 (2x+16)=112$

$\qquad\quad {:}\longmapsto\sf (2x+16) 7=112$[/tex]

$\qquad\quad {:}\longmapsto\sf 2x+16=\cancel{{\dfrac {112}{7}}}$

$\qquad\quad {:}\longmapsto\sf 2x+16=16$

$\qquad\quad {:}\longmapsto\sf 2x=16-16$

$\qquad\quad {:}\longmapsto\sf 2x=0$

$\qquad\quad {:}\longmapsto\sf x={\dfrac {1}{2}}$

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Shorter parallel side=${\dfrac {1}{2}}=0.5cm$

Larger parallel side=$16+0.5=16.5cm$

Answer 2

Height of a trapezium=14cm

Let

the shorter parallel side=x

The larger parallel side=x+16

As we know that in a Trapezium

${\boxed{\sf Area={\dfrac {1}{2}}\times (sum\:of\:parallel\:sides)×height}}$

Substitute the values

$\qquad\quad {:}\longmapsto\sf {\dfrac {1}{2}}(x+x+16)×14=112$

$\qquad\quad {:}\longmapsto\sf {\dfrac {1}{\cancel{2}}}(2x+16)×\cancel {14}=112$

$\qquad\quad {:}\longmapsto\sf 7 (2x+16)=112$

$\qquad\quad {:}\longmapsto\sf (2x+16) 7=112$[/tex]

$\qquad\quad {:}\longmapsto\sf 2x+16=\cancel{{\dfrac {112}{7}}}$

$\qquad\quad {:}\longmapsto\sf 2x+16=16$

$\qquad\quad {:}\longmapsto\sf 2x=16-16$

$\qquad\quad {:}\longmapsto\sf 2x=0$

$\qquad\quad {:}\longmapsto\sf x={\dfrac {1}{2}}$

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Shorter parallel side=${\dfrac {1}{2}}=0.5cm$

Larger parallel side=$16+0.5=16.5cm$✅