Question

he area of a trapezium is 280 sq. cm and its height is 35 cm. If one of its parallel

sides is longer than the other by 10 cm, find the lengths of the two parallel sides​

Answer 1

Answer :-

• The two parallel sides of trapezium are 3cm and 13cm.

Step-by-step explanation:

To Find :-

• The lengths of two parallel sides of trapezium

Solution:

Given that,

• The area of trapezium = 280cm²
• The height of trapezium = 35cm
• One parallel side of trapezium is longer than the other by 10cm.

Assumption: Let us assume the length of shorter parallel side of trapezium as "(x) centimetres" and the longer side of trapezium ( longer by 10cm ) as "(x+10) centimetres",

As we know that,

Area of trapezium = 1/2 × ( a + b ) × h,

Where,

• a and b are the two parallel sides of trapezium.
• h is the distance between them.

Therefore,

• 1/2 × { x + ( x + 10 ) } × 35 = 280

=> 1/2 × { x + ( x + 10 ) } × 35 = 280

=> 1/2 × { x + x + 10 } × 35 = 280

=> 1/2 × { 2x + 10 } × 35 = 280

=> 1 × 2x + 10 × 35 = 280 × 2

=> 2x + 10 × 35 = 560

=> 2x + 10 = 560/35

=> 2x + 10 = 16

=> 2x = 16 - 10

=> 2x = 6

=> x = 6/2

=> x = 3

Now,

The length of shorter parallel side :

• ( x ) cm = 3cm

The length of longer parallel side :

• ( x + 10 ) cm = ( 3 + 10 ) cm = 13cm

Hence, The two parallel sides of trapezium are 3cm and 13cm.

Answer 2

Given :-

$~$

• The two parallel sides of trapezium are 3 cm and 13 cm.

$~$

To find :-

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• The length of two parallel sides of trapezium.

$~$

Solution :-

$~$

• The area of trapezium
• The height of trapezium
• One parallel side of trapezium is longer than the other by 10 cm.

$~$

Assumption : Let us assume the length of shorter parallel side of trapezium as " (x) centimetres " and the longer side of trapezium (longer by 10cm) as " (x + 10) centimetres ",

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$~~~~~~~~~~~~~~~~$ ★ We know that :

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• Area of trapezium = ${\sf{\frac{1}{2} \times (a + b) \times h}}$

$~$

$~~~~~~~~~~~$ ________________________

• a and b are the two parallel sides of trapezium.

• h is the distance between them.

$~~~~~~~~~~~$ ________________________

$~$

$\implies$$\large{\sf{\frac{1}{2} \times x + (x + 10) \times 35 = 280}}$

$~$

$\implies$ $\large{\sf{\frac{1}{2} \times x + (x + 10) \times 35 = 28}}$

$~$

$\implies$ $\large {\sf{\frac{1}{2} \times 2x + 10 \times 35 = 280}}$

$~$

$\implies$ $\large{\sf{1 \times 2 + 10 \times 35 = 280 \times 2}}$

$~$

$\implies$ $\large{\sf{2x + 10 \times 35 = 560}}$

$~$

$\implies$ $\large{\sf{2x + 10 = \frac{560}{35} }}$

$~$

$\implies$ $\large{\sf{2x + 10 = 16}}$

$~$

$\implies$ $\large{\sf{2x = 16 - 10}}$

$~$

$\implies$ $\large{\sf{2x = 6}}$

$~$

$\implies$ $\large{\sf{x = \frac{6}{2}}}$

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$\implies$ $\large{\sf{x = \dfrac{\cancel{6}}{\cancel{2}}}}$

$~$

$\implies$$\large{\underline{\boxed{\red{\bf{x~=~3}}}}}$$\purple\bigstar$

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$\large\dag$ Hence

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❍ The length of shorter parallel side :

• (x) cm = 3cm

❍ The length of longer parallel side :

• (x + 10) cm = (3 + 10) cm = 13 cm

$~$

$\large\dag$ Hence Verified

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• The two parallel sides of trapezium are 3 cm and 13 cm.