Question

A figure is in the form of a quadrilateral ABCD its
area is 155 cm2. Find the length of the perpendicular
drawn from Don AC if AC = 15 cm and length of
perpendicular from B on AC is 12 cm.
(1) 10 cm
1220​

Answer 1

Answer:

ANSWER

Area of quadrilateral =

2

1

d(h

1

+h

2

)

165cm

2

=

2

1

×15(12+d)

330=180+15d

15d=150=

15

150

=10cm

Answer 2

Answer:

Diagram:-

$\setlength{\unitlength}{1.2 cm}\begin{picture}(0,0)\linethickness{0.4mm}\qbezier(0,0)(0,0)(1,3)\qbezier(4.6,1)(4.6,1)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(4.6,1)(4.6,1)(0,0)\qbezier(4,3)(4,3)(0,0)\qbezier(4.6,1)(4.6,1)(3,2.25)\qbezier(2,1.5)(2,1.5)(1,3)\qbezier(2.2,1.7)(2.2,1.7)(2.05,1.9)\qbezier(2.05,1.9)(2.05,1.9)(1.82,1.74)\qbezier(3.25,2.4)(3.25,2.4)(3.44,2.25)\qbezier(3.44,2.25)(3.44,2.25)(3.25,2.05)\put(-0.4,-0.5){\sf C}\put(4.8,0.6){\sf B}\put(4.2,3.2){\sf A}\put(0.4,3){\sf D}\end{picture}$

Given:-

Area of a Quadiratral =155cm ${}^{2}$

AC=15cm

Length of perpendicular drawn from B on AC =12cm

To find:-

Length of perpendicular drawn from D on AC

Solution:-

Here if you simplify the concept then we get

• Diagonal 's length=15cm
• Length of one perpendicular drawn from opposite vertice=12cm

We need to find the length of Other perpendicular .

• Let it be x

As we know that in a Quadiratral

${\boxed{\sf Area=\dfrac {1}{2}\times Diagonal\times sum\:of\:the \;length\;of\:perpendiculars \:drawn\:from\:opposite\:vertices}}$

• Substitute the values

${:}\rightarrowtail$$\sf 155=\dfrac {1}{2}\times 15 \times (12+x)$

• Simplify

${:}\rightarrowtail$$\sf 155=\dfrac {15 (12+x)}{2}$

${:}\rightarrowtail$$\sf 155=\dfrac {180+15x}{2}$

• use cross multiplication

${:}\rightarrowtail$$\sf 2 (155)=180+15x$

${:}\rightarrowtail$$\sf 310=15x+180$

${:}\rightarrowtail$$\sf 15x=310-180$

${:}\rightarrowtail$$\sf 15x=130$

${:}\rightarrowtail$$\sf x=\dfrac{130}{15}$

${:}\rightarrowtail$$\sf x=8.6cm$

$\therefore\underline{\underline{\sf Length \:of\:the\:perpendicular\:drawn\:from\:D\:on\:AC\:is \:8.6cm.}}$