# NCERT Class 10 Chapter 7 Triangles Official CBSE Board Sample Problems Short Answer

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## Question

is right angled at C. If p is the length of the perpendicular from C to AB and a, b, c are the lengths of the sides opposite respectively then prove that

### Solution

Given: In and .

Also, and

To prove:

Proof: In

Apply Pythagoras theorem

(i)

Now, area of (ii)

Also area of ...(iii)

Equation (iii) and (ii) we have

Put value of in equation (i)

(dividing both sides by )

## Question

From airport two aero planes start at the same time. If the speed of first aero plane due North is 500 km/h and that of other due East is 650 km/h, then find the distance between two aero planes after 2 hours.

### Solution

Speed of aero plane along north = 500 km/h

Speed of aero plane along east = 650 km/b

Distance travelled by aero plane in 2 hours in

North direction.

Distance travelled by aeroplane in 2 hours in East direction.

Distance between both d’ roplanes after 2 hours =AB.

(By Pythagoras theorem in ]

km

## Question

R and S are points on the sides DE and EF respectively of a LDEF such that and . Find whether or not.

### Solution

Construction: Join RS

To find: or not

Proof: WE have RE = 5 cm

and RD = 2.5 cm

Now

Similarly, we have,

and

Now,

Here

RS is not parallel to DF.

## Question

In the figure, ABCD is a parallelogram and E divides BC in the ratio 1:3. DB and AE intersect at F. Show that DF = 4FB and AF = 4FE

### Solution

Given ABCD is a parallelogram and

To show DF=4FB and AF=4FE

Proof In and

(Alternate angles)

(V. O. A.)

(by AA)

AS

Put in (I), we get

AND

## Question

If the areas of two similar triangles are equal, prove that they are congruent.

### Solution

Given, area and

We know that:

Similarly BC = QR and AC = PR

Thus, SSS congruency criterion)

## Question

In fig, if D is mid-point of BC, find the value of

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