Question

ABCD is a trapezium of area 91 cm square CD is parallel to a b and CD is longer than ab and CD longer than ab by 8 cm if the distance between ab and cd is 7 cm find ab and Cd​

Answer 1

Reference of trapezium is in attachment.

AnswEr:-

Parallel sides of trapezium are 9 cm & 17 cm respectively.

$\rule{200}{1}$

Let the parallel sides be m & n cm respectively.

↠ n - m = 8

↠ n = m + 8 - - -(Eq.1)

Now we know,

☛ Area of trapezium = ½ × (Sum of parallel sides) × Distance

• Putting values:-

⇒ 91 = ½ (m + n) × 7

⇒ ½ (m + m + 8) = 91/7

$\scriptsize\sf{\: \: \: \: \: \: \: \: \: \: \: \: \big[\because n = m + 8 \big]}$

⇒ ½ (2m + 8) = 13

⇒ ½ × 2(m + 4) = 13

⇒ m + 4 = 13

⇒ m = 13 - 4

⇒ m = 9

∴ One parallel side = 9 cm

Now putting value of m in (Eq.1)

⇒ n = 9 + 8

⇒ n = 17

∴ Another parallel side = 17 cm

Therefore,

$\therefore\underbrace{\textsf{PARALLEL SIDES ARE ={\textbf{ 9 cm \& 17 cm }}}}$

Answer 2

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{1.2cm}\begin{picture}(8,2)\thicklines\put(8.6,3){\large{A}}\put(7.7,0.9){\large{D}}\put(9,1.4){\bf{\large{Area = 91 cm^\bf2 }}}\put(13.1,0.9){\large{C}}\put(11.8,0.7){\large{M}}\put(8,1){\line(1,0){5}}\put(12,1){\line(0,2){2}}\put(9,3){\line(3,0){3}}\put(11.2,2){\sf{\large{7 cm}}}\put(13,1){\line(-1,2){1}}\put(8,1){\line(1,2){1}}\put(12.1,3){\large{B}}\end{picture}$

$\rule{160}{1}$

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$:\implies\tt Area_{trapezium}=\dfrac{1}{2} \times (Sum\:of\:Parallel\:Sides) \times Height\\\\\\:\implies\tt 91=\dfrac{1}{2} \times (AB+CD) \times BM\\\\\\:\implies\tt 91 \times 2 = (AB+CD) \times 7\\\\\\:\implies\tt \dfrac{91 \times 2}{7} = (AB+CD)\\\\\\:\implies\tt 13 \times 2 = (AB+CD)\\\\\\:\implies\tt 26 = (AB+CD)\\\\ {\scriptsize\qquad\bf{\dag}\:\:\textsf{Given that : \bf{CD = (AB + 8)}}}\\\\:\implies\tt 26 = AB + AB + 8\\\\\\:\implies\tt 26 - 8 = 2AB\\\\\\:\implies\tt 18 = 2AB\\\\\\:\implies\tt \dfrac{18}{2} = AB\\\\\\:\implies\tt AB = 9\:cm$

$\rule{180}{2}$

$\underline{\bigstar\:\:\textsf{Parallel Sides :}}$

$\bullet\:\:\textsf{AB = \textbf{9 cm}}\\\bullet\:\:\textsf{CD = (AB + 8) = (9 + 8) = \textbf{17 cm}}$