Question

The area of a trapezium is 850 sq. cm. One of the parallel sides is 64 cm and the perpendicular
distance between the parallel sides is 17 cm. Find the length of other parallel side. ​

Answer 1

Given :

Area of trapezium = 850 sq.m

Length of one of the parallel sides = 64 cm

Perpendicular distance between the parallel sides = 17 cm

To Find :

The length of the other parallel side

Solution :

Area of a trapezium is given by ,

$\\ \star \: {\boxed{\purple{\sf{Area_{(trapezium)} = \frac{1}{2} \times (a + b) \times d}}}}$

Here ,

a and b are length of parallel sides

h is distance between the parallel sides

We have ,

a = 64 cm

A = 850 sq.m

d = 17 cm

Substituting the values ;

$\\ : \implies \sf \: 850 = \frac{1}{2} \times (64 + b) \times 17$

$\\ : \implies \sf \: 850 \times 2 = (64 +b) \times 17$

$\\ : \implies \sf \: 1700 = (64 + b) \times 17$

$\\ : \implies \sf \: \frac{1700}{17} = 64 + b$

$\\ : \implies \sf \: 64 + b = 100$

$\\ : \implies \sf \: b = 100 - 64$

$\\ : \implies {\underline{\boxed{\pink{\mathfrak{b = 36 \: cm}}}}} \: \bigstar$

Hence ,

The length of the other parallel side is 36 cm

Answer 2

Given:

• Area of trapezium = 850 cm².
• Length of one parallel side of trapezium = 64 cm
• Perpendicular distance between the parallel sides = 17 cm

To find:

• Length of other parallel side?

Solution:

☯ Let length of other parallel side of trapezium be x cm.

⠀⠀⠀⠀

$\setlength{\unitlength}{1.3cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf D }\put(-0.3,-0.3){ \bf B }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf 17\ cm }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf 64\ cm }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf x\ cm }\end{picture}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

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

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

Where,

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

⠀⠀⠀⠀

$\sf We\:have \begin{cases} & \sf{Area_{\:(trapezium)} = \bf{850\:cm^2}} \\ & \sf{Length\:of\:one\: parallel\:side\:, a = \bf{64\:cm}} \\ & \sf{Distance\:between\:two\: parallel\:sides\:, h = \bf{17\:cm}} \end{cases}$

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

$:\implies\sf \dfrac{1}{2} \times (64 + x) \times 17 = 850$

$:\implies\sf (64 + x) \times 17 = 850 \times 2$

$:\implies\sf (64 + x) \times 17 = 1700$

$:\implies\sf (64 + x) = \cancel{ \dfrac{1700}{17}}$

$:\implies\sf (64 + x) = 100$

$:\implies\sf x = 100 - 64$

$:\implies{\underline{\boxed{\frak{\purple{x = 36\:cm}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Length\:of\:other\: parallel\:side\:is\: {\textsf{\textbf{36\:cm}}}.}}}$