Question

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.

Answer 1

Answer:

• Length of bases are 15 cm and 21 cm.

Step-by-step explanation:

To find :-

• Length of bases.

Solution :-

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

Answer 2

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,

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

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

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

⇒ $\sf 2x + 6 \times 7 =\: 252$

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

⇒ $\sf 2x + 6 =\: 36$

⇒ $\sf 2x =\: 36 - 6$

⇒ $\sf 2x =\: 30$

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

➠ $\sf\bold{\pink{x =\: 15\: cm}}$

Hence, the required length of bases are :

$\longmapsto$ One base of a trapezium :

$\implies$ $\sf x\: cm$

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

$\longmapsto$ Other base of a trapezium :

$\implies$ $\sf x + 6\: cm$

$\implies$ $\sf 15 + 6\: cm$

$\implies$ $\sf\bold{\red{21\: cm}}$

$\therefore$ The length of the bases of a trapezium is 15 cm and 21 cm respectively.