Question

the area of trapezium is 475 cm ² and the heightis 19cm find the length of its two parallel sides , if one side is 4 cm greater than other​

Answer 1

Given: The area of trapezium is 475 cm² and the height is 19 cm.

Need to find: The length of its two parallel sides.

❒ Let the smaller side of trapezium is x cm and Larger side is (x + 4) cm.

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$\qquad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: According \ to \ the \ Question \: :}}}}}\mid}$⠀

• The area of the given trapezium is 475 cm².⠀

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$\underline{\bf{\dag} \:\mathfrak{As \: we \; know \; that\: :}}$⠀

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$\star\:\boxed{\sf{\pink{Area_{\:(trapezium)} = \dfrac{1}{2} \times sum \: of \; || \; sides \times Height}}}$

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Therefore,

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$:\implies\sf 475 = \dfrac{1}{2} \times \Big(x + (x + 4) \Big) \times 19\\\\\\:\implies\sf 475 = \dfrac{1}{2} \times \Big(2x + 4 \Big) 19 \\\\\\:\implies\sf \dfrac{\cancel{475}}{\cancel{19}} = \dfrac{1}{2} \times \Big(2x + 4 \Big)\\\\\\:\implies\sf 25 = \dfrac{1}{2} \times \Big(2x + 4 \Big)\\\\\\:\implies\sf 50 = 2x + 4\\\\\\:\implies\sf 2x = 50 - 4\\\\\\:\implies\sf 2x = 46\\\\\\:\implies\sf x = \cancel\dfrac{46}{2}\\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 23}}}}}\:\bigstar$

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Hence,

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• Smaller side, x = 23 cm

• Larger side, (x + 4) = (23 + 4) = 27 cm

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$\therefore\:{\underline{\sf{Hence, \ the \ length \; of \: || \; sides \; of \; trapezium \: are \: \bf{23 \: cm \: and \: 27 \; cm}.}}}$

Answer 2

Answer:

Given :-

• The area of trapezium is 475 cm² and the height is 19 cm and if one side is 4 cm greater than other.

To Find :-

• What is the length of two parallel sides.

Formula Used :-

${\red{\boxed{\small{\bold{Area\: of\: trapezium\: =\: \dfrac{1}{2} \times Sum\: of\: parallel\: sides\: \times Height}}}}}$

Solution :-

Let, the smaller side be x cm

And, the greater side will be x + 4 cm

Given :

• Area of trapezium = 475 cm²
• Height = 19 cm

According to the question by using the formula we get,

⇒ $\sf \dfrac{1}{2} \times x + x + 4 \times 19 =\: 475$

⇒ $\sf \dfrac{1}{2} \times 2x + 4 \times 19 =\: 475$

⇒ $\sf \dfrac{1}{2} \times 2x + 4 =\: \dfrac{\cancel{475}}{\cancel{19}}$

⇒ $\sf \dfrac{1}{2} \times 2x + 4 =\: 25$

⇒ $\sf 2x + 4 =\: 25 \times 2$

⇒ $\sf 2x + 4 =\: 50$

⇒ $\sf 2x =\: 50 - 4$

⇒ $\sf 2x =\: 46$

⇒ $\sf x =\: \dfrac{\cancel{46}}{\cancel{2}}$

➠ $\sf\bold{\purple{x =\: 23\: cm}}$

Hence, the required parallel sides are,

✧ Smaller side = x = 23 cm

✧ Greater side = x + 4 = 23 + 4 = 27 cm

$\therefore$ The two parallel sides of a trapezium is 23 cm and 27 cm.