Question

The area of a quadrilateral is 180 cm square. The length of the perpendicular drawn from the opposite vertices on the diagonal are 6 cm and 14 cm respectively.Find the length of the diagonal.​

Answer 1

$\setlength{\unitlength}{1 cm}\begin{picture}(20,15)\thicklines \qbezier(1,1)(1,1)(6,1)\qbezier(1,1)(1,1)(1.6,4) \qbezier(1.6,4)(1.6,4)(6.6,4)\qbezier(6,1)(6,1)(6.6,4)\qbezier(6.6,4)(6.6,4)(1,1)\qbezier(1.6,4)(1.6,4)(6,1)\put(0.7,0.5){\sf A}\put(6,0.5){\sf B}\put(1.4,4.3){\sf D}\put(6.6,4.3){\sf C}\end{picture}$

Let 'O' be the point of intersection of the Diagonals AC and BD

Given:

• Area of ABCD = 180 cm²

• OD = 6 cm

• OB = 14 cm

To Find:

Length of AC = ?

Method:

Quadrilateral ABCD can be divided into 2 Triangles namely ABC and ACD

Area of Δ ABC = $\dfrac{1}{2} \times AC \times OB$

Area of Δ ABC = $\dfrac{1}{2}$ × AC × 14 = 7 AC →→→→→ (Equation 1)

Area of Δ ACD = $\dfrac{1}{2}$ × AC × OD = $\dfrac{1}{2} \times AC \times 6 = 3AC \longrightarrow (Equation \: 2)$

Area of ABCD = Area of Δ ABC + Area of Δ ACD

⇒ Area of ABCD = 7 AC + 3 AC = 180 cm²

⇒ 10 AC = 180 or AC = $\dfrac{180}{10}$ = 18 cm

AC = 18 cm

Length of Diagonal = 18 cm.

Answer 2

Answer:

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