Question

10. The measures of the bases of a

trapezoid are x2 – 19 and 10. The
measure of the midsegment is 8.
Find the value of x.

Answer 1

The value of x is 2
`√(29)` .

Explanation:

Given as :

The area of Trapezoid = x² unit²

The measure of base 1 =
`b_1` = - 19 unit

The measure of base 2 =
`b_2` = 10 unit

The height of the mid segment = 8 unit

Now, From the Area of Trapezoid

i.e Area =
`(1)/(2)` × (sum of opposite base) × height

Or, x² =
`(1)/(2)` × (19 + 10) × 8

Or, x² =
`(8)/(2)` × (29)

Or, x² = 4 × (29)

Or, x² = 116

∴ x =
`√(116)`

I.e x = 2
`√(29)`

Hence, The value of x is 2
`√(29)` . Answer