In the triangle ACB Line AP divides the two triangles APB and ACP-If Area of - APB -24 cm 2 and Area - APB - Area of - APC -4- 7- find the area of - APCA- 42 cm 2B- 36 cm 2C- 54 cm 2D- 48 cm 2

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Ratio of Areas of Triangles Having Common Vertex and Bases in a Straight Line

In the triang...

Question

In the triangle ACB Line AP divides the two triangles APB and ACP.

If Area of $Δ$ APB = $24 c m^{2}$ and Area $Δ$ APB : Area of $Δ$ APC = 4 : 7, find the area of $Δ$ APC

$42 c m^{2}$

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$54 c m^{2}$

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$36 c m^{2}$

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$48 c m^{2}$

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Solution

The correct option is A
$42 c m^{2}$

Area of $Δ$ APB : Area of $Δ$ APC = 4 : 7

Area of $Δ$ APB = 4x and Area of $Δ$ APC = 7x

4x = 24

$\Rightarrow$ x = 6

$∴$ Area of Triangle APC = 7x = 7 $\times$ 6 = $42 c m^{2}$

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In the triangle ACB Line AP divides the two triangles APB and ACP. If Area of Δ APB = 24 cm2 and Area Δ APB : Area of Δ APC = 4 : 7, find the area of Δ APC

The correct option is A 42cm2 Area of Δ APB : Area of Δ APC = 4 : 7 Area of Δ APB = 4x and Area of Δ APC = 7x 4x = 24 ⇒ x = 6 ∴ Area of Triangle APC = 7x = 7×6 = 42cm2

In the triangle ACB Line AP divides the two triangles APB and ACP.

If Area of $Δ$ APB = $24 c m^{2}$ and Area $Δ$ APB : Area of $Δ$ APC = 4 : 7, find the area of $Δ$ APC

The correct option is A
$42 c m^{2}$

Area of $Δ$ APB : Area of $Δ$ APC = 4 : 7

Area of $Δ$ APB = 4x and Area of $Δ$ APC = 7x

4x = 24

$\Rightarrow$ x = 6

$∴$ Area of Triangle APC = 7x = 7 $\times$ 6 = $42 c m^{2}$