Question

the area of a quadrilateral is 342 sq.CM the perpendicular from two of its opposite vertices to the diagonal are 12 m & 12m. what is the length of the diagonal?

Answer 1

Answer:

Given :

Area of quadrilateral ABCD= 342 m²

BE= 12 m , DF= 12 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

342= 1/2AC(BE+DF)

342 = 1/2×AC (12+12)

342×2= 24AC

AC= (342×2)/24

AC = 342/12= 28.5 m

Hence, the length of the diagonal is 28.5 m

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