Question

the area of a trapezium is 270 cm2 and the altitude is 9 cm.If one of the parallel sides is 6 cm longer than the other,find the length of both parallel sides.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

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• Area of the Trapezium = 270 cm²
• Height of the Trapezium = 9 cm
• One parallel side 6 cm longer than the other parallel side .

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• Length of both parallel sides = ?

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$\maltese$ According to the Question :

$\longmapsto$ Let the 2nd parallel side be y .So,

$\qquad \; {\pmb{\sf{ 1st \; Parallel \; Side = a = y \; cm }}}$

$\longmapsto$ 1st parallel side 6 cm longer than the 2nd parallel side .So,

$\qquad \; {\pmb{\sf{ 2nd \; Parallel \; Side = b = y + 6 \; cm }}}$

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$\maltese$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Area{\small_{(Trapezium)}} = \dfrac{1}{2} \times \bigg( a + b \bigg) \times Height }}}}}$

Where :

• a = 1st parallel side
• b = 2nd parallel side

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$\maltese$ Calculating the Value of y :

${\longmapsto{\qquad{\sf{ Area = \dfrac{1}{2} \times \bigg( a + b \bigg) \times Height }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 270 = \dfrac{1}{2} \times \bigg\{ \bigg( y + 6 \bigg) + y \bigg\} \times 9 }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 270 = \dfrac{1}{2} \times \bigg( 2y + 6 \bigg) \times 9 }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \dfrac{270}{9} = \dfrac{1}{2} \times \bigg( 2y + 6 \bigg) }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \cancel\dfrac{270}{9} = \dfrac{1}{2} \times \bigg( 2y + 6 \bigg) }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 30 = \dfrac{1}{2} \times \bigg( 2y + 6 \bigg) }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 30 \times 2 = 1 \times \bigg( 2y + 6 \bigg) }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 60 = 2y + 6 }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 60 - 6 = 2y }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 54 = 2y }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \dfrac{54}{2} = y }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \cancel\dfrac{54}{2} = y }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\red{\frak{ y = 27 }}}}}}}}$

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$\maltese$ Calculating the Parallel sides :

• 1st parallel side = y + 6 = 27 + 6 = 33 cm
• 2nd parallel side = y = 27 cm

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$\maltese$ Therefore :

❛❛ Two parallel sides of the Trapezium are 27 cm and 33 cm . ❜❜

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