Question

the parallel sides of the trapezium are 7 more and 7 less than the distance between them. find their lengths and distance between them, if the area of the trapezium is 169 m²​

Answer 1

Given: Area or trapezium is 169 m².

To find: Length and distance between parallel sides (height) ?

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☯ Let the distance between parallel sides be x m.

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

• The parallel sides of the trapezium are 7 more and 7 less than the distance between them or height of trapezium.

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Therefore,

One parallel side is 7 more than Height = x + 7

Other parallel side is 7 less than height = x - 7

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Area_{\;(trapezium)} = \dfrac{1}{2} \times (a + b) \times h}}}}$

where,

• a & b are two parallel sides and h is the height of trapezium or distance between two parallel sides.

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$\dag\;{\underline{\frak{Now,\:Putting\:values\:in\:formula,}}}$

$:\implies\sf \dfrac{1}{2} \times \bigg[(x + 7) + (x - 7) \bigg] \times x = 169\\ \\ \\ :\implies\sf \dfrac{1}{ \cancel{2}} \times \cancel{2}\:x \times x = 169\\ \\ \\ :\implies\sf x^2 = 169\\ \\ \\ :\implies\sf \sqrt{x^2} = \sqrt{169}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{x = 13}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Distance\:between\:two\:parallel\:sides\:is\: {\textsf{\textbf{13\:m}}}.}}}$

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$\dag\;{\underline{\frak{Now,\:Sides\:of\: trapezium\:are,}}}$

• One of the parallel side, (x + 7) = 13 + 7 = 20 m
• Another parallel side, (x - 7) = 13 - 7 = 6 m

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$\therefore\:{\underline{\sf{Length\:of\:two\: parallel\:sides\:is\:20\:m\:and\:6\:m.}}}$

Answer 2

Answer:

Given :-

• The parallel sides of the trapezium are 7 more and 7 less than the distance between them.
• The area of the trapezium is 169 m².

To Find :-

• What is the parallel sides of the trapezium.

Formula Used :-

★ Area of trapezium = ½ × Sum of parallel sides × h ★

Solution :-

Let, the height or parallel sides be x

Hence,

Other parallel side is 7 more than the distance be x + 7

And, the other parallel side is 7 less than the distance will be x - 7

Given :

• Area of trapezium = 169 m²

According to the question by using the formula we get,

↦ ½ × (x + 7) + (x - 7) × x = 169

↦ ½ × 2x × x = 169

↦ x² = 169

↦ x = √169

➠ x = 13

Hence, the required parallel sides are,

✧ One of the parallel sides = x + 7 = 13 + 7 = 20 m

✧ Another parallel sides = x - 7 = 13 - 7 = 6 m

∴ The length of two parallel sides are 20 m and 6 m .