Question

Find the value of t in the diagram

Answer 1

In a trapezoid, with bases $b$ and $B$ and height $h$, the area is given by

$A = \frac{(B+b)h}{2}$

In your case:

$B = BC = 3t$

$b = AD = t$

$h = AB = t$

so, the formula becomes

$A = \frac{(3t+t)t}{2} = \frac{4t^2}{2} = 2t^2$

Since the area is $50 \text{cm}^2$, we have

$2t^2 = 50 \iff t^2 = 25 \iff t = 5$

Answer 2

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