Question

The area of a trapezium is 110 cm squares and it’s height is 10cm.If one of the parallel sides is longer than the other by 8 cm,find the length of the two parallel sides.


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Answer 1

Given :-

• The area of a trapezium is 110 cm squares and it’s height is 10cm.If one of the parallel sides is longer than the other by 8 cm.

To find :-

• Length of the two parallel sides.

Solution :-

• Area of a trapezium = 110cm²
• Distance between parallel sides (h) = 10cm

Now, let the parallel sides of a triangle be x and (x + 8)

According to question

→ Area of trapezium = 110cm²

→ ½ × sum of parallel sides × height = 110

→ ½ × (a + b) × h = 110

→ ½ × (x + x + 8) × 10 = 110

→ 5(2x + 8) = 110

→ 10x + 40 = 110

→ 10x = 110 - 40

→ 10x = 70

→ x = 70/10

→ x = 7

Hence,

• Measures of parallel sides
• First parallel side = x = 7cm
• Second parallel side = (x + 8) = 15cm

Verification :-

• h = 10cm
• a = 7cm
• b = 15cm

Substitute all the values

→ Area of trapezium

→ ½ × (a + b) × h

→ ½ × (7 + 15) × 10

→ 5 × 22

→ 110 cm²

Hence, verified

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The area of a trapezium = 110cm²

• The height of the trapezium = 10cm

• One of the parallel sides is longer than the other by 8cm.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The length of the two parallel sides.

$\bf{\underline{\underline\green{Solution:-}}}$

One of the parallel sides is longer than the other by 8cm.

Let one of the parallel sides be x cm

The other parallel side = (x + 8)cm

Area of trapezium = 110cm²

Height of the trapezium = 10cm

As we know that:-

Area of the trapezium is given by the formula

$\boxed{ \rm Area \: of \: trapezium = \frac{1}{2} \times (sum \: of \: parallel \: sided) \times height}$

Substituting the values:-

${ \rm \implies 110= \dfrac{1}{2} \times (x + x + 8) \times 10}$

${ \rm \implies 110= \dfrac{1}{2} \times (2x+ 8) \times 10}$

${ \rm \implies 110= \dfrac{1}{ \cancel2} \times (2x+ 8) \times \cancel{10} \: \large ^{5} }$

${ \rm \implies 110= 5(2x + 8) }$

${ \rm \implies \dfrac{110}{5} = (2x + 8) }$

${ \rm \implies 22 = (2x + 8) }$

${ \rm \implies 22 - 8= 2x }$

${ \rm \implies 14= 2x }$

${ \rm \implies x = \dfrac{14}{2} }$

${ \rm \implies x = 7}$

Length of one of the parallel lines = x = 7cm

Length of the other parallel line

= x + 8

= 7 + 8

= 15cm

$\underline{ \boxed{ \purple{\rm \therefore Th e \: lengths \: of \: parallel \: sides \: are \: 7cm \: and \: 15cm}}}$