Question

8. The area of a trapezium is 450 cm^2 If its one parallel side is 10 cm more than the other and the distance between them is 10 cm, find the two parallel sides.​

Answer 1

Question:-

The area of a trapezium is 450 cm². If its one parallel side is 10 cm more than the other and the distance between them is 10 cm, find the two parallel sides.

Answer:-

• First parallel side (a) is 40 cm
• 40 cmSecond parallel side (b) is 50 cm

Given:-

• Area of trapezium= 450 cm²
• First parallel side (a) = x cm
• Second parallel side (b) = x + 10 cm
• Height (h) = 10 cm

To find:-

• Length of parallel sides

Solution:-

$\boxed{ \large{area = \frac{a + b}{2} \times h}}$

$\implies \: \frac{x + x + 10}{2}\times 10 = 450 \\ \\ \implies \: \frac{2x + 10}{2} = \frac{450}{10 } \\ \\ \implies \: 2x + 10 = 45 \times 2 \\ \\ \implies \: 2x = 90 - 10 \\ \\ \implies \: x = \frac{80}{2} \\ \\ \implies \: x = 40$

• First parallel side (a) = x = 40 cm
• Second parallel side (b) = x + 10 = 40 + 10= 50 cm

Answer 2

Given

• Area of trapezium = 450 cm²
• It's one parallel side is 10 cm more than the other.
• The distance between them, i.e., height of the trapezium is 10 cm.

To find

• The two parallel sides of the trapezium.

Solution

• Let the first parallel side be x.
• Then, the another parallel side will be (x + 10)cm.

Now,

$\underline{\boxed{\tt{Area\: of\: trapezium = \dfrac{Sum\: of\: parallel\: sides}{2} × height}}}$

⠀

$\tt:\implies{Area = \dfrac{Side\: A + Side\: B}{2} × h}$

⠀

$\tt:\implies{450 = \dfrac{x + (x + 10)}{2} × 10}$

⠀

$\tt:\implies{450 = \dfrac{2x + 10}{\not{2}} × \not{10}}$

⠀

$\tt:\implies{450 = 2x + 10 × 5}$

⠀

$\tt:\implies{\dfrac{450}{5} = 2x + 10}$

⠀

$\tt:\implies{90 = 2x + 10}$

⠀

$\tt:\implies{90 - 10 = 2x}$

⠀

$\tt:\implies{2x = 80}$

⠀

$\tt:\implies{x = \dfrac{80}{2}}$

⠀

$\tt:\implies{\underline{\boxed{\orange{x = 40}}}}$

⠀

$\rule{200}3$

⠀

• First parallel side = x = 40cm
• Second parallel side = (x + 10) ⠀⠀⠀= 50cm