Question

The area of traperium is 182 cm2.
Its height is 14cm . The larger parallel
side is longer than the other by
16cm . Find the length of the parallel
sides.​

Answer 1

Answer:

given area of trapezium 182cm2

Step-by-step explanation:

let smaller parallel side=x

larger=x+16

ar=1/2(×+×+16)*14

182=(2×+16)×7

182=14×+112

14×=70

×=5

larger side is 16+5=21

Answer 2

$\textbf{\huge{\underline{Given:}}}$

● Area of Trapezium = 182 cm^2

● Height = 14 cm

● One parallel side is longer than other by 16 cm

$\textbf{\huge{\underline{To\:Find:}}}$

Length of the parallel sides

$\textbf{\huge{\underline{Solution:}}}$

$\star$ Let the one parallel side be a and other be a+16

We know that :

$\star \sf\: Area \: of \: Trapezium = \dfrac{1}{2} (Sum \: of \: parallel \: sides) \times height$

$\hookrightarrow \sf \: 182 {cm}^{2} = \dfrac{1}{2} (a + a + 16) \times 14 \: cm$

$\hookrightarrow \sf \: 182 {cm}^{2} = \dfrac{1}{ \cancel2} (2a + 16) \times \cancel14$

$\hookrightarrow \sf \: 182 {cm}^{2} = 7(2a + 16)$

$\hookrightarrow \sf \: 182 {cm}^{2} = 14a + 112$

$\hookrightarrow \sf \: 14a = 182 - 112$

$\hookrightarrow \sf \: 14a = 70$

$\hookrightarrow \sf \: a = \dfrac{70}{14}$

$\hookrightarrow \sf \: a = \large \boxed{ \sf \: 5 \: cm}$

Now,

$\star \: \sf \: Measure \: of \: 1 \: parallel \: side = 5 \: cm$

$\star \: \sf \: Other \: Parallel \: Side \: = 5 + 16 \\ = \sf \: 21 \: cm$

$\textbf{\huge{\underline{Verification:}}}$

$\sf\: Area \: of \: Trapezium = \dfrac{1}{2} (Sum \: of \: parallel \: sides) \times height$

$\hookrightarrow \sf \: Area = \dfrac{1}{ \cancel2} (5 + 21) \times \cancel 14$

$\sf \hookrightarrow \:Area = 7(5 + 21)$

$\sf \hookrightarrow \:Area = 35 + 147$

$\sf \hookrightarrow \:Area = \large \boxed{ \sf \: 182 \: {cm}^{2} }$

Hence,Verified!