Question

The area of a quadrilateral is 3432 sq. cm. The perpendiculars from two vertices to the diagonal are 13 cm and 19 cm . What is the length of its diagonal?​

Answer 1

Answer:

Step-by-step explanation:

Solution:

Given :

Area of quadrilateral ABCD= 3432 m²

BE= 13 m , DF= 19 m

Let ABCD be a quadrilateral & AC be one of its diagonal.

BE perpendicular AC & DF perpendicular AC

Area of quadrilateral ABCD= ar∆ABC + ar∆ADC

Area of quadrilateral ABCD= 1/2×AC×BE + 1/2×AC×DF

3432= 1/2AC(BE+DF)

3432 = 1/2×AC (13+19)

3432×2= 32AC

AC= (3432×2)/32

AC = 6864/32= 214.5 m

Hence, the length of the diagonal is 214.5 m

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