Question

the area of a quadrilateral shaped field is 252cm² the perpendiculars dropped on it fro the opposite corners on a diagonal are 8m and 13m find the length of a diagonal

Answer 1

✬ Length of Diagonal = 24 m ✬

Step-by-step explanation:

Given:

• Area of quadrilateral shaped field is 252 cm².
• Perpendiculars dropped on diagonal are 8 m and 13 m.

To Find:

• What is the length of the diagonal of quadrilateral?

Solution: We know that the area of quadrilateral:-

★ Area of quadrilateral = 1/2 x Diagonal x (Sum of perpendiculars ) ★

But area given is 252 m².

A/q

$\implies{\rm }$ 252 = 1/2 x diagonal x ( 8 + 13 )

$\implies{\rm }$ 252 = 1/2 x diagonal x 21

$\implies{\rm }$ 252 x 2 = diagonal x 21

$\implies{\rm }$ 504 = diagonal x 21

$\implies{\rm }$ 504/21 = diagonal

$\implies{\rm }$ 24 m = Diagonal

Hence, The length of diagonal of quadrilateral is 24 m.

________________

★ Verification ★

➪ 1/2 x 24 x ( 13 + 8 ) m² = 252 m²

➪ 12 x 21 m² = 252 m²

➪ 252 m² = 252 m² { Verified }