The area of a trapezium is 126cm. The height of the trapezium is 7cm. If one of the bases is longer than the other by 6cm, find the length of the bases About the author Alaia
Answer: Given :- The area of a trapezium is 126 cm². The height of the trapezium is 7 cm. One of the base is longer than the other by 6 cm. To Find :- What is the length of the bases. Formula Used :- [tex]{\underline{\boxed{\mathcal{\pmb{\quad \bigstar \: Area\: of\: Trapezium =\: \dfrac{1}{2} \times Sum\: of\: parallel\: sides\: \times Height\quad}}}}} [/tex] Solution :- Let, the one base be x cm And, the other base be x + 6 cm Given : Area of trapezium = 126 cm² Height of trapezium = 7 cm According to the question by using the formula we get, [tex]⇒ \sf \dfrac{1}{2} \times x + x + 6 \times 7 =\: 126 [/tex] [tex]⇒ \sf \dfrac{1}{2} \times 2x + 6 \times 7 =\: 126 [/tex] [tex]⇒ \sf 2x + 6 \times 7 =\: 126 \times 2[/tex] [tex]⇒ \sf 2x + 6 \times 7 =\:252[/tex] [tex]⇒ \sf 2x + 6 =\: \dfrac{\cancel{252}}{\cancel{7}}[/tex] [tex]⇒ \sf 2x + 6 =\: 36[/tex] [tex]⇒ \sf 2x =\: 36 – 62x[/tex] [tex]⇒ \sf 2x =\: 30[/tex] [tex]⇒ \sf x =\: \dfrac{\cancel{30}}{\cancel{2}}[/tex] [tex]➠ \sf\bold{\pink{x =\: 15\: cm}}[/tex] Hence, the required length of bases are : ⟼ One base of a trapezium : [tex]⟹ \sf x\: cm[/tex] [tex]\implies \sf\bold{\red{15\: cm}}[/tex] ⟼ Other base of a trapezium : [tex]\implies \sf x + 6\: cmx[/tex] [tex]⟹ \sf 15 + 6\: cm[/tex] [tex]⟹ \sf\bold{\red{21\: cm}}[/tex] ∴ The length of the bases of a trapezium is 15 cm and 21 cm respectively. Reply
Step-by-step explanation: Given that, Area of trapezium is 126 cm². Height of trapezium is 7 cm. Let, Other base be x cm. And One base be x + 6 cm. If the height 7 cm have two bases and height is of trapezium then the x and x + 6 are parallel sides of trapezium. We know, Area of trapezium = (a + b)/2 × h Put area, height and bases (parallel sides) of trapezium in formula : \longrightarrow⟶ 126 = (x + x + 6)/2 × 7 \longrightarrow⟶ 126 × 2 = 2x + 6 × 7 \longrightarrow⟶ 252 = 2x + 6 × 7 \longrightarrow⟶ 252/7 = 2x + 6 \longrightarrow⟶ 36 = 2x + 6 \longrightarrow⟶ 36 – 6 = 2x \longrightarrow⟶ 30 = 2x \longrightarrow⟶ 30/2 = x \longrightarrow⟶ x = 15 Length of bases :- One base = x + 6 = 15 + 6 = 21 cm Other base = x = 15 cm Reply
Answer:
Given :-
The area of a trapezium is 126 cm². The height of the trapezium is 7 cm. One of the base is longer than the other by 6 cm.
To Find :-
What is the length of the bases.
Formula Used :-
[tex]{\underline{\boxed{\mathcal{\pmb{\quad \bigstar \: Area\: of\: Trapezium =\: \dfrac{1}{2} \times Sum\: of\: parallel\: sides\: \times Height\quad}}}}} [/tex]
Solution :-
Let, the one base be x cm
And, the other base be x + 6 cm
Given :
Area of trapezium = 126 cm²
Height of trapezium = 7 cm
According to the question by using the formula we get,
[tex]⇒ \sf \dfrac{1}{2} \times x + x + 6 \times 7 =\: 126 [/tex]
[tex]⇒ \sf \dfrac{1}{2} \times 2x + 6 \times 7 =\: 126 [/tex]
[tex]⇒ \sf 2x + 6 \times 7 =\: 126 \times 2[/tex]
[tex]⇒ \sf 2x + 6 \times 7 =\:252[/tex]
[tex]⇒ \sf 2x + 6 =\: \dfrac{\cancel{252}}{\cancel{7}}[/tex]
[tex]⇒ \sf 2x + 6 =\: 36[/tex]
[tex]⇒ \sf 2x =\: 36 – 62x[/tex]
[tex]⇒ \sf 2x =\: 30[/tex]
[tex]⇒ \sf x =\: \dfrac{\cancel{30}}{\cancel{2}}[/tex]
[tex]➠ \sf\bold{\pink{x =\: 15\: cm}}[/tex]
Hence, the required length of bases are :
⟼ One base of a trapezium :
[tex]⟹ \sf x\: cm[/tex]
[tex]\implies \sf\bold{\red{15\: cm}}[/tex]
⟼ Other base of a trapezium :
[tex]\implies \sf x + 6\: cmx[/tex]
[tex]⟹ \sf 15 + 6\: cm[/tex]
[tex]⟹ \sf\bold{\red{21\: cm}}[/tex]
∴ The length of the bases of a trapezium is 15 cm and 21 cm respectively.
Step-by-step explanation:
Given that,
Area of trapezium is 126 cm².
Height of trapezium is 7 cm.
Let, Other base be x cm.
And One base be x + 6 cm.
If the height 7 cm have two bases and height is of trapezium then the x and x + 6 are parallel sides of trapezium.
We know,
Area of trapezium = (a + b)/2 × h
Put area, height and bases (parallel sides) of trapezium in formula :
\longrightarrow⟶ 126 = (x + x + 6)/2 × 7
\longrightarrow⟶ 126 × 2 = 2x + 6 × 7
\longrightarrow⟶ 252 = 2x + 6 × 7
\longrightarrow⟶ 252/7 = 2x + 6
\longrightarrow⟶ 36 = 2x + 6
\longrightarrow⟶ 36 – 6 = 2x
\longrightarrow⟶ 30 = 2x
\longrightarrow⟶ 30/2 = x
\longrightarrow⟶ x = 15
Length of bases :-
One base = x + 6 = 15 + 6 = 21 cm
Other base = x = 15 cm