Question

pel sides are 15 m and 13 m long
40. The difference between the lengths of the parallel sides of a trapezium
is 8 cm, the perpendicular distance between these sides is 24 cm and the
area of the trapezium is 312 cm'. Find the length of each of the parallel
sides,
41. A parallele​

Answer 1

ɢɪᴠᴇɴ :-

Difference between parallel sides = 8cm

Distance between parallel sides = 24cm

Area of Trapezium = 312 cm²

ᴛᴏ ғɪɴᴅ :-

• Length of parallel sides

sᴏʟᴜᴛɪᴏɴ :-

Let one parallel side(Smaller) be x cm then, second parallel side(larger) is (8 + x) cm

Now,

We know that,

• Area of Trapezium = ½ × (Sum of parallel sides) × (distance between them)

➮ 312 = ½ × {x + (x + 8)} × 24

➮ 312 × 2 = (2x + 8) × 24

➮ 624 = (2x + 8) × 24

➮ 624/24 = 2x + 8

➮ 26 = 2x + 8

➮ 2x = 26 - 8

➮ 2x = 18

➮ x = 18/2

➮ x = 9

Hence,

• One parallel side = x = 9 cm
• Second parallel side = (x + 8) = 9 + 8 = 17cm

Answer 2

$\sf{\underline{Answer\::}}$

Length of the parallel sides of the trapezium are,

1. x = 17 cm
2. y = 9 cm

$\sf{\underline{Explanation\::}}$

The difference between the measures of the two parallel sides of the trapezium is 8 cm.

And,the height of the trapezium is 24 cm. The area of this trapezium is 312 cm².

Solve for the length of the two parallel sides.

We can assume,

1. First parallel side as x cm.
2. Second parallel side as y cm.

The difference between the sides x and y is given as 8 cm.

Our 1st equation,

1. x - y = 8

Now further it is given about the area of the trapezium.

It is known that the formula of area of trapezium is,

• $\bold{Area\:of\: trapezium\:=\:\dfrac{1}{2}\:(sum\:of\: parallel\:sides\:)\:\times\: height}$

The area is already given as 312 cm² and we also know the height,24 cm.

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

=> $\sf{312\:=\:(x+y)\:\times\:12}$

=> $\sf{312\:=\:12x+12y}$

=> $\sf{\dfrac{312}{12}\:=x+y}$

=> $\sf{26\:=x+y\;\;\;\;\;\;(2)}$

Simultaneously solve first and second equation. Add equations (1) and (2).

=> $\sf{x-y+x+y=8+26}$

=> $\sf{2x=34}$

=> $\sf{x=\dfrac{34}{2}}$

=> $\sf{x=17}$

We know,x is the length of the first parallel side. Using value of x in equation (1) we can find length of other parallel side too.

=> $\sf{x-y=8}$

=> $\sf{17-y=8}$

=> $\sf{-y=8-17}$

=> $\sf{-y=-9}$

=> $\sf{y=9}$

•°• The length of parallel sides of the trapezium of height 24 cm and area 312 cm² are : 17 cm and 9 cm.