Question

In a trapezium one of the parallel side is twice the other if the area of the trapezium is 252 cm and its altitude is 20 CM then find the measure of The parallel side ​

Answer 1

AnswEr :

⋆ Reference of Image is in the attachment :

The Two Parallel Sides of Trapezium ABCD are AB and CD, with Altitude CM of 20 cm.

Let the Side CD be x cm, and Other Parallel Side AB be 2x cm i.e. twice the Other Side.

• According to the Question Now :

⇒ Area = 1 /2 × (Sum of || Sides) × Altitude

⇒ Area × 2 = (AB + CD) × CM

⇒ 252 cm² × 2 = (2x + x) × 20 cm

⇒ 504 cm² = 3x × 20 cm

⇒ 504 cm² = 60x cm

• Dividing Both term by 60 cm

⇒ x = 8.4 cm

◗ CD = x cm = 8.4 cm

◗ AB = 2x cm = 2(8.4) cm = 16.8 cm

∴ Parallel Sides are 8.4 cm and 16.8 cm.

_________________________________

• Verification :

⇒ Area = 1 /2 × (Sum of || Sides) × Altitude

⇒ Area = 1 /2 × (AB + CD) × CM

⇒ 252 cm² = 1 /2 × (8.4 + 16.8) × 20 cm

⇒ 252 cm² = 25.2 cm × 10 cm

⇒ 252 cm² = 252 cm² ⠀⠀Hence, Verified!

Answer 2

$\bf{\Huge{\underline{\boxed{\mathfrak{\pink{ANSWER\::}}}}}}$

$\bf{\Large{\underline{\rm{\red{Given\::}}}}}$

In a trapezium one of the parallel side is twice the other if the area of the trapezium is 252cm² & it's altitude is 20cm.

$\bf{\Large{\underline{\sf{\yellow{To\:find\::}}}}}}$

The measures of the parallel side.

$\bf{\Large{\underline{\sf{\green{Explanation\::}}}}}$

We have,

• Let the length of the one parallel side be 2R
• Let the length of the other parallel side be R
• Area of the trapezium= 252cm²
• Altitude of the trapezium= 20cm

We know that formula of the area of trapezium;

⇒ ${\frac{1}{2} *(sum\: of \:parallel \:side)*height}$    [sq.units]

A/q

→ $\frac{1}{2} *(2R+R)*20cm=252cm^{2}$

→ $\frac{1}{\cancel{2}} *(3R)*\cancel{20}cm=252cm^{2}$

→ 3R × 10cm = 252cm²

→ 30R = 252cm²

→ R = $\cancel{\frac{252cm^{2} }{30cm} }$

→ R = 8.4cm

Now,

• The measures of the parallel sides:

One of the parallel side= 2R= (2×8.4)cm= 16.8cm

Other of the parallel side= R=8.4cm