The area of a quadrilateral is 227.2. One of its diagonals is the lengths of the perpendiculars placed by the vertices before it is 7.2 and 8.8. What is the length of its diagonal?
Answers
If the area of the quadrilateral is 227.2 and the perpendicular lengths are 7.2 and 8.8 then the length of its diagonal is 28.4 unit.
Step-by-step explanation:
The area of the quadrilateral = 227.2 sq. unit
The perpendicular lengths drawn from the two vertices on to one of its diagonals are 7.2 unit and 8.8 unit.
Let the length of the diagonal of the quadrilateral be denoted as “x” unit.
The formula of the area of a quadrilateral is given as,
Area = ½ * [length of one of its diagonal] * [sum of the lengths of the perpendicular drawn from it on the remaining two vertices]
Now, substituting the given values into the above formula, we get
227.2 = ½ * x * [7.2 + 8.8]
⇒ 227.2 = ½ * x * [16]
⇒ 227.2 = 8 * x
⇒ x = 227.2/8
⇒ x = 28.4 unit
Thus, the length of the diagonal of the quadrilateral is 28.4 unit.
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