You visited us 1 times! Enjoying our articles? Unlock Full Access!

If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

The vertices ...

Question

The vertices of a $Δ$ ABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB at D, such that AD/AB= $\frac{1}{4}$ . Calculate the area of the $Δ$ ADC.

Open in App

Solution

So D is the point which divides AB in the ratio 1: 3.

Using section formula we get the coordinates of D(3.25,5.75)

Area of a triangle = $\frac{1}{2}$ [ $x_{1}$ ( $y_{2}$ - $y_{3}$ ) + $x_{2}$ ( $y_{3}$ - $y_{1}$ ) + $x_{3}$ ( $y_{1}$ - $y_{2}$ )]

= $\frac{1}{2}$ [4(5.75 - 2) +3.25(2 - 6) + 7(6 - 5.75)]

= 1.875 sq units

Suggest Corrections

Similar questions

Q. The vertices of a

Δ A B C

are A(4,6), B(1,5) and C(7,2). A line is drawn to intersect sides AB and AC at D and E respectively, such that

\frac{A D}{A B} = \frac{A E}{A C} = \frac{1}{4}

. Calculate the area of the

Δ A D E

and compare it with the area of

Δ A B C

. (Recall Theorem 6.2 and Theorem 6.6).

Q. In the figure, the vertices of

A B C

are

A (4, 6), B (1, 5)

and

C (7, 2) .

A line-segment

D E

is drawn to intersect the sides

A B

and

A C

D

and

E

respectively such that

\frac{A D}{A B} = \frac{A E}{A C} = \frac{1}{3}

. Calculate the area of

Δ A D E

The vertices of a $Δ A B C$ are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that
$\frac{A D}{A B} = \frac{A E}{A C} = \frac{1}{4}$ . Calculate the ratio of the area of the $Δ A D E$ and $Δ A B C$ .