Question

The area of a trapezium is 168 cm² and its height is 8 cm. If one of the parallel sides is longer than the other by 6
cm. find the length of each of the parallel sides​

Answer 1

CORRECT question :-

→ The area of trapezium is 168 cm² and it's height is 8 cm. If one of the parallel side is longer than other by 6 cm. Find the length of each of the parallel sides.

$\huge\underline\green{\tt Solution: }$

Let one parallel side be ' x ' cm then, other will be  ' x + 6 ' cm.

Area of trapezium = $\dfrac{1}{2}$ ( sum of parallel sides ) × height

According to question

$\dfrac{1}{2}$ ( x + x + 6 ) × 8 = 168

⇒ ( 2x + 6 ) × 4 = 168

⇒ 2x + 6 = $\dfrac{168}{4}$

⇒ 2x + 6 = 42

⇒ 2x = 42 - 6

⇒ 2x = 36

⇒ x= $\dfrac{36}{2}$

∴ x = 18

Now,

other will be 18 + 6 = 24 cm

Answer:   one of the parallel side is 18 cm and other will be 24 cm.

$\huge\underline\green{\tt Verification : }$

$\dfrac{1}{2}$ ( 18 + 24 ) × 8  = 168

⇒ $\dfrac{1}{2}$ ( 42 ) × 8  = 168

⇒ 42 × 4 = 168

⇒ 168 cm² = 168 cm²

L.H.S = R.H.S

____________________

$\huge\mathscr\red{Be\:brainly!!!}$

Answer 2

Let one parallel side be ' x ' cm then, other will be ' x + 6 ' cm.

We know,

Area of trapezium = $\frac{1}{2}$ ×( sum of parallel sides ) × height

According to question

$\frac{1}{2}$( x + x + 6 ) × 8 = 168

⇒ ( 2x + 6 ) × 4 = 168

⇒ 2x + 6 = $\frac{168}{4}$

⇒ 2x + 6 = 42

⇒ 2x = 42 - 6

⇒ 2x = 36

⇒ x= $\frac{36}{2}$

∴ x = 18

Now,

Other side will be 18 + 6 = 24 cm

Answer: One of the parallel side is 18 cm and other side is 24 cm.