Question

Find the value of t in the diagram

Answer 1

5 cm

Step-by-step 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

Answer 2

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

`A = ((B+b)h)/(2)`

In your case:

`B = BC = 3t`

`b = AD = t`

`h = AB = t`

so, the formula becomes

`A = ((3t+t)t)/(2) = (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`