Question

THE area of a trapezium is 280cmsquare and its height is 35 cm.if one of its parallel sides is longer than the other by 10cm,find the lengths of the two parallel sides​

Answer 1

Given : The Area of the Trapezium is 280 cm² and one of its Parallel side is 10 cm Longer than the other parallel side . Height of the Trapezium is 35 cm .

To Find : Find the Length of the Parallel Sides

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SolutioN :

$\dag$ According to the Question :

$\longmapsto$ Let the Smaller Parallel Side be y .So :

$\qquad \; {\pmb{\sf{ Smaller \; Parallel \; Side = y \; cm }}}$

$\longmapsto$ Longer Parallel Side is 10 cm longer than the Smaller Parallel Side .So :

$\qquad \; {\pmb{\sf{ Longer \; Parallel \; Side = y + 10 \; cm }}}$

$\dag$ Formula Used :

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

Where :

• a = Smaller Parallel Side
• b = Longer Parallel Side

$\dag$ Calculating the Value of y :

${\longmapsto{\qquad{\sf{ Area = \dfrac{1}{2} \times \bigg( a + b \bigg) \times Height }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 280 = \dfrac{1}{2} \times \bigg\{ y + \bigg( y + 10 \bigg) \bigg\} \times 35 }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 280 \times 2 = 1 \times \bigg\{ y + \bigg( y + 10 \bigg) \bigg\} \times 35 }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 560 = 1 \times \bigg\{ y + \bigg( y + 10 \bigg) \bigg\} \times 35 }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 560 = \bigg\{ y + \bigg( y + 10 \bigg) \bigg\} \times 35 }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 560 = \bigg( 2y + 10 \bigg) \times 35 }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \dfrac{560}{35} = 2y + 10 }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \cancel\dfrac{560}{35} = 2y + 10 }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 16 = 2y + 10 }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 16 - 10 = 2y }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 6 = 2y }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \dfrac{6}{2} = y }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \cancel\dfrac{6}{2} = y }}}} \\ \\ \\ \\ \ {\qquad \; \; {\longmapsto \;{\underline{\boxed{\pmb{\pink{\frak{ y = 3 }}}}}}}} \; {\green{\pmb{\bigstar}}}$

$\dag$ Calculating the Parallel Sides :

• 1st Parallel Side = y = 3 cm
• 2nd Parallel Side = y + 10 = 3 + 10 = 13 cm

$\therefore \;$ The two Parallel Sides are 3 cm and 13 cm .

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Answer 2

Answer:

The two Parallel Sides are 3 cm and 13 cm .

Step-by-step explanation:

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