Question

The difference between the two parallel sides of a Trapezium is 8 metres the perpendicular distance between them is 24 metres and the area of trapezium is 312 square metres then its longer side is

Answer 1

Step-by-step explanation:

Given:-

• The difference between the two parallel sides of a Trapezium is 8m.

• The perpendicular distance between them is 24m.

• The area of trapezium is 312m²

To Find:-

• The longer side of the trapezium.

Solution:-

Let the parallel sides of the trapezium be x and y

Let x be the longer side, i.e x > y

Given, the difference between the sides is 8m

So:-

$\sf \dashrightarrow x - y = 8.....(i)$

Now, The perpendicular distance ( Height ) = 24m

The area of trapezium = 312m²

$\sf Area \: of \: trapezium = \dfrac{1}{2}\times (sum\: of \: parallel\: sides) \times Height$

$\sf \implies 312 = \dfrac{1}{2}\times (x + y) \times 24$

$\sf \implies 312 = (x + y) \times 12$

$\sf \implies 312 = 12(x + y)$

$\sf \implies (x + y) = \dfrac{312}{12}$

$\sf \dashrightarrow x + y = 26......(ii)$

$\sf Now, \: Adding \: equations \: (i) and (ii)$

$\sf \implies x - y + x + y = 8 + 26$

$\sf \implies 2x = 34$

$\sf \implies x = \dfrac{34}{2}=17$

Longer side = x = 17

$\large\underline{\boxed{\purple{\rm \therefore The \: longer\: side = 17m}}}$

Answer 2

Question :-

the difference between the two parallel sides of a Trapezium is 8m . the perpendicular distance between them is 24 and the area of trapezium is 312 square metres then find its longest side ?

Solution :-

Given ,

• the difference between the two parallel side is 8 metre .
• the perpendicular distance between them is 24 .
• the area of trapezium is 312 square metre .

what we have to find here ?

=> we have to find here the longest side of the trapezium .

Answer :-

Let The parallel side of the trapezium be x and y .

The longest side be "x" .

it is given in the question that the difference between the two side is 8 m .

Now,

x-y=8.........(eq-1)

the height is 24 m .

the area of trapezium is 312 metre square .

Now,

| area of trapezium = 1/2 ×(sum of parallel side) × height |

So,

substituting the value .

=>312 = 1/2 ×(x+y)×24

=>312 = (x+y)×12

=>(x+y)=312/12

=>(x+y)=26 ......(eq-2)

now adding the equation1 and equation 2 we get ;

=> x+y+x-y = 26+8

=> 2x = 34

=> x = 34/2

=> x = 17 m .

Hence,

the longest side of the trapezium is 17 m .