Question

12)The parallel sides of a trapezium are in the ratio 5:3. The area is 112
sq.cm, if the height is 14 cm, the sides of the trapezium are
O 5,3
O 10,6
O 15,9
○20, 12​

Answer 1

Step-by-step explanation:

Answer:-

Given:-

• The parallel dives as ratio of 5:3
• The area of parallelogram as 112 cm²
• The height of the trapezium is 14 cm

To find:-

• The sides of the trapezium

Let's Try!

First of all, when we are given with the requirements that means there is a use. First step is to assume a ratio constant as x .

So, we need to know that

$\sf{Area \ of \ Trapezium = \dfrac{1}{2} \times (Sum \ of \ Parallel \ sides) \ height }$

Extend $\longrightarrow$

So, let's place the values.

$\sf{112 = \dfrac{1}{2} \times (5x + 3x ) \times 14 }$

$\sf{112 = \dfrac{1}{2} \times (8x ) \times 14 }$

$\sf{112 = 8x \times 7 }$

$\sf{112 = 8x \times 7 }$

$\sf{\dfrac{112}{8 \times 7} = x }$

$\sf{ x = 2 }$

So, placing the values of x now,

• 5x = 5 × 2 = 10
• 3x = 3 × 2 = 6

So, the sides are 10 and 6 cm respectively.

Answer 2

Answer:

Given :-

• Parallel sides are in ratio 5:3
• Area = 112 cm²
• Height = 14 cm

To Find :-

Parallel sides

SoluTion :-

As we know that

Let the parallel sides be 5x and 3x

• Area of a trapezoid = ½ (sum of parallel sides) Height

112 = ½(5x + 3x) × 14

112 = 14/2 (8x)

112 = 7(8x)

112 = 56x

x = 112/56

x = 2

Parallel sides are

• 5(2) = 10 cm
• 3(2) = 6 cm

$\huge \tt \: Option B$