Math, asked by Fake3636, 3 months ago

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​

Answers

Answered by usjadhav2001
1

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

Answered by Anonymous
3

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 :-

{\underline{\boxed{\mathcal{\pmb{\quad \bigstar \: Area\: of\: Trapezium =\: \dfrac{1}{2} \times Sum\: of\: parallel\: sides\: \times Height\quad}}}}}

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,

⇒ \sf \dfrac{1}{2} \times x + x + 6 \times 7 =\: 126

⇒ \sf \dfrac{1}{2} \times 2x + 6 \times 7 =\: 126

⇒ \sf 2x + 6 \times 7 =\: 126  \times 2

⇒ \sf 2x + 6 \times 7 =\:252

⇒ \sf 2x + 6 =\: \dfrac{\cancel{252}}{\cancel{7}}

⇒ \sf 2x + 6 =\: 36

⇒ \sf 2x =\: 36 - 62x

⇒ \sf 2x =\: 30

⇒ \sf x =\: \dfrac{\cancel{30}}{\cancel{2}}

➠ \sf\bold{\pink{x =\: 15\: cm}}

Hence, the required length of bases are :

⟼ One base of a trapezium :

⟹ \sf x\: cm

\implies \sf\bold{\red{15\: cm}}

⟼ Other base of a trapezium :

\implies \sf x + 6\: cmx

⟹ \sf 15 + 6\: cm

⟹ \sf\bold{\red{21\: cm}}

∴ The length of the bases of a trapezium is 15 cm and 21 cm respectively.

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