Question

17. The lengths of the parallel sides of a trapezium are (x + 9) cm and (2x - 3)cm, and
distance between them is (x + 4) cm. If its area is 540 cm2, find x.​

Answer 1

Given

we have given the area of trapezium which is 540cm²& length of the parallel sides of a trapezium are (x+9)cm & (2x-3)cm

and distance between the || sides is (x+4)cm

To Find

we have to find the value of x

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Area of trapezium = sum of parallel sides × height ÷2

Note :The Distance between the parallel sides will be considered as height of the trapezium.

=>540= (x+9)+(2x-3)×(x+4)÷2

=>540= (x+9+2x-3)(x+4)÷2

=>540×2= (3x+6)(x+4)

=>3x(x+4)+6(x+4)=1080

=>3x²+12x+6x+24=1080

=>3x²+18x+24=1080

taking 3 common

=>x²+6x+8=360

=>x²+6x=352

=>x²+6x-352=0

Now ,it is the form of a quadratic equation so,we simply factorise it to find the value of x.

By using quadratic formula

x= -b ± √b²-4ac ÷2

x= -6±√6²-4(1)(-352)/2

x=-6±√36-(-1408)/2

x=-6±√36+1408/2

x=-6±√1444/2

here,the discriminant b²-4ac is >0

So,it have two real roots

x=-6±38/2

x=32/2 or x=-44/2

x=16 or x= -22

since,Area can't be negative so, we take positive value of x

Therefore, x = 16 is the correct answer

Extra information=>

Properties of Trapezium:

• Trapezium having two parallel sides and two non-parallel sides.
• Sum of all the angles in a trapezium is 360°.