Find the length of a diagonal of a quadrilateral whose area is $195 m^{2}$ and the lengths of the perpendicular to the diagonal vertices are $8.5 m$ and $11 m$ respectively.

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Solution

The area of quadrilateral is $195 c m^{2}$
The length of perpendicular heights are $8.5$ and $11$
The area of quadrilateral is given by $\frac{1}{2} \times d \times (h_{1} + h_{2})$
where $d$ is length of diagonal
$h_{1} = 8.5; h_{2} = 11$
$⟹ 195 = \frac{1}{2} \times d \times (11 + 8.5) 195 = \frac{1}{2} \times d \times 19.5 10 = \frac{1}{2} \times d d = 2 \times 10 d = 20$

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Find the length of a diagonal of a quadrilateral whose area is 195 m2 and the lengths of the perpendicular to the diagonal vertices are 8.5 m and 11 m respectively.

The area of quadrilateral is 195cm2The length of perpendicular heights are 8.5 and 11The area of quadrilateral is given by 12×d×(h1+h2)where d is length of diagonal h1=8.5;h2=11⟹195=12×d×(11+8.5)195=12×d×19.510=12×dd=2×10d=20

Find the length of a diagonal of a quadrilateral whose area is $195 m^{2}$ and the lengths of the perpendicular to the diagonal vertices are $8.5 m$ and $11 m$ respectively.