Question

the area of a trapeziem768cm2. its altitude is 16cm and one of the parallel side is 10cm longer than the other. find the length of the parallel .
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Answer 1

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

● Area of Trapezium = 768 cm^2

● Altitude(Height) = 16 cm

● One of the parallel side = 10 cm

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

● Length of the parallel sides

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

Let one parallel side be a and other be (a+10) cm

$\star \rm \: Area \: of \: Trapezium = \dfrac{1}{2} (a + b) \times h$

(a + b refers to the sum of parallel sides)

$\sf \hookrightarrow \:768 {cm }^{2} =\dfrac{1}{2} (a + a + 10) \times 16$

$\sf \hookrightarrow768 {cm}^{2} = \: \dfrac{1}{ \cancel2} (2a+ 10) \times \cancel 16$

$\hookrightarrow \sf 768 {cm}^{2} = \: 8(2a + 10)$

$\hookrightarrow \sf768 {cm }^{2} = \: 16a + 80$

$\sf \hookrightarrow - 16a = 80 - 768$

$\hookrightarrow \sf \: - 16a = -688$

$\hookrightarrow \sf \: a = \cancel\dfrac{ - 688}{ - 16}$

$\hookrightarrow \sf \: a = 43 \: cm$

$\star \rm \: Length \: of \: 1st \: parallel \: side = 43 \: cm$

$\star \rm \: Length \: of \: other \: parallel \: side = 43 + 10 \\ = \sf \: 53cm$

Answer 2

Step-by-step explanation:

Given

the area of trapezium=768cm²

altitude of trapezium=16cm

let

one of the parallel side be X

and other parallel side X+10

As we know that,

Area of trapezium=1/2{sum of parallel side s}*Altitude

so,

$\frac{1}{2}(x + x + 10) \times 16 = 76</em></strong><strong><em>8</em></strong><strong><em>\\ \\ \frac{1}{2} (2x + 10) \times 16 = 76</em></strong><strong><em>8</em></strong><strong><em> \\ \\(2x + 10) \times 8 = 76</em></strong><strong><em>8</em></strong><strong><em>\\ \\ 16x + 80 = 76</em></strong><strong><em>8</em></strong><strong><em>\\ \\ 16x = 76</em></strong><strong><em>8</em></strong><strong><em> - 80 \\ \\ 16x = </em></strong><strong><em>6</em></strong><strong><em>8</em></strong><strong><em>8</em></strong><strong><em> \\ \\ x = </em></strong><strong><em>4</em></strong><strong><em>3</em></strong><strong><em>$

Hence:

the one of parallel side=43cm

the other parallel side=53cm

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