the area of a trapezium is 168cm^2 and the length of one of the parallel sides is 30 cm and height is 8 cm. find the length of the other parallel side
Answers
Step-by-step explanation:
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: }
Solution:
Let one parallel side be ' x ' cm then, other will be ' x + 6 ' cm.
Area of trapezium = \dfrac{1}{2}
2
1
( sum of parallel sides ) × height
According to question
\dfrac{1}{2}
2
1
( x + x + 6 ) × 8 = 168
⇒ ( 2x + 6 ) × 4 = 168
⇒ 2x + 6 = \dfrac{168}{4}
4
168
⇒ 2x + 6 = 42
⇒ 2x = 42 - 6
⇒ 2x = 36
⇒ x= \dfrac{36}{2}
2
36
∴ 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 : }
Verification:
\dfrac{1}{2}
2
1
( 18 + 24 ) × 8 = 168
⇒ \dfrac{1}{2}
2
1
( 42 ) × 8 = 168
⇒ 42 × 4 = 168
⇒ 168 cm² = 168 cm²
L.H.S = R.H.S
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