Question

h=(x - 4)

b=(2x + 1)

a=x

area of trapezium is 33 m

Answer 1

Given,
h = (x - 4)
b = (2x + 1)
a = x
Area of trapezium = 33 m

We know that,

Area of trapezium = a + b/2 × h
=> 33 = x+(2x+1)/2 × (x-4)
=> 33 = x+2x+1/2×x-4
=> 33 = 3x+1/2×x-4
=> 33 = (3x+1)(x-4)/2
=> 33×2 = 3x^2-12x+x-4
=> 66 = 3x(x-4)+1(x-4)
=> 66 = (3x+1)(x-4)

Now,
3x+1 = 66 or, x-4 = 66
=>3x = 66-1 =>x = 66+4
=>x = 65/3 =>x = 70

So,
a = x
= 70 m

b = 2x+1
= 2×70+1
= 140+1
= 141 m

h = x-4
= 70-4
= 66 m