Question

3. In the given figure, find AC if the area of the
quadrilateral ABCD is 3,600 sq m.
35 m​

Answer 1

Answer:

• We Can See that Diagonal AC is Dividing Quadrilateral ABCD into Two Parts.
• ∆ ABC and ∆ ACD will be formed with common Base AC.

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$:\implies\tt Ar.\:ABCD=Ar.\:ABC+Ar.\:ACD\\\\\\:\implies\tt Ar.\:ABCD=\bigg(\dfrac{1}{2} \times Base \times Height\bigg)+\bigg(\dfrac{1}{2} \times Base \times Height\bigg)\\\\\\:\implies\tt 3600 = \dfrac{1}{2} \times Base \times (35 + 65)\\\\\\:\implies\tt 3600 = \dfrac{1}{2} \times Base \times 100\\\\\\:\implies\tt 3600 = Base \times 50\\\\\\:\implies\tt \dfrac{3600}{50} = Base\\\\\\:\implies\underline{\boxed{\textsf{\textbf{Base = 72 m (AC)}}}}$

Answer 2

AnswEr:-

Length of AC = 72 m

$\rule{200}{1}$

Here in the attachment,we can see:-

☛ Altitude of ∆ABC = 35 m

☛ Altitude of ∆ADC = 65 m

☛Area of quadrilateral ABCD =3600 m²

☛ Diagonal (AC) = ?

Here,AC divides ABCD into two same triangles.

We know,

☛ Area of triangle = ½ × Base × Height

According to question:-

⇒ Area(ABCD) = Area[∆ABC + ∆ADC]

⇒ 3600 = ½ × B × H + ½ × B × H

⇒ 3600 = ½ × AC × 35 + ½ × AC × 65

$\scriptsize\sf{\: \: \: \: \: \: \:\: \: \: \: \: \: \big[\because Base \: of \: both \: \triangle = AC \big]}$

⇒ 3600 = ½ AC (35 + 65)

⇒ 3600 = ½ AC( 100)

⇒ 3600 = 50AC

⇒ AC = 3600/50

⇒ AC = 72 m

Therefore,

$\therefore\underline{\textsf{LENGTH OF AC = {\textbf{72 m }}}}$