Respuesta :

In a trapezoid, with bases [tex] b [/tex] and [tex] B [/tex] and height [tex] h [/tex], the area is given by


[tex] A = \frac{(B+b)h}{2} [/tex]


In your case:


[tex] B = BC = 3t [/tex]

[tex] b = AD = t [/tex]

[tex] h = AB = t [/tex]


so, the formula becomes


[tex] A = \frac{(3t+t)t}{2} = \frac{4t^2}{2} = 2t^2 [/tex]


Since the area is [tex] 50 \text{cm}^2 [/tex], we have


[tex] 2t^2 = 50 \iff t^2 = 25 \iff t = 5 [/tex]

smmwaite

Answer


5 cm



Explanation

The figure shown is a trapezium.

The area of a trapezium is given by;


Area = 1/2 h( a+b)

Where h ⇒perpendicular distance between the two parallel sides 

a and b ⇒length of the parallel sides.

h = t

a =t

b = 3t


1/2 t(t+3t) = 50

1/2 ×t × 4t = 50

1/2 ×4t²=50

2t² = 50

dividing both sides by 2

t² = 25

t = √25

= 5 cm

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