Question

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.​

Answer 1

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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