area of a quadilateral is 336 cm².the sum of the altitudes drawn on to a diagonal is 21 cm.find the length of the diagonal.
Answers
Answered by
2
Step-by-step explanation:
420= 1/2 (9+12) d
420= 2= 21×d
d= 420×2/21
d= 40cm
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Answered by
18
Answer:
Area of quadrilateral = 336 sq cm
Area of triangles (as soon as you draw the diagonal, you see two triangles in the figure) = 336/2
The triangles which are found after the diagonal is drawn are equal in area. Thus, each has area of = 168 sq cm
Area of triangle = 1/2 × b × h = 168
Base is same for both triangles. Let the height be = x and y
=> 1/2 × b × x = 168
=> x = 336/b __(1)
=> 1/2 × b × h = 168
=> y = 336/b __(2)
(1) + (2) = 21
x + y = 21
=> (336/b)2 = 21
=> b = 672/21
=> b = 32 cm
Thus, diagonal is equal to 32 cm.
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