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State true or false.

Draw five triangles and measure their sides. Is in each case the sum of the length of any two sides is always less than the third side?

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True

False

answer is B.

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Detailed Solution

Draw first triangle

△ ABC

with three side lines AB, BC and CA.
Question Image

The sides on measure we get,

AB = 4.7 cm,

BC = 5.5 cm

AC = 3.4 cm

Here,

AB + BC

= 4.7 cm + 5.5 cm

= 10.2 cm

AS,

10.2 > 3.4

. Thus,

AB + BC > AC

Now,

△ PQR

On measuring the sides, we get,

PQ = 2.8 cm,

QR = 4 cm

PR = 4.1 cm

Here,

PQ + QR

= 2.8 cm + 4 cm

= 6.8 cm

Since,

6.8 > 4.1,

So,

PQ + QR > PR

Third triangle

△ XYZ

can be drawn as,
Question Image

Here,

XY = 2.4 cm,

YZ = 5 cm

ZX = 5.5 cm

XY + YZ

= 2.4 cm + 5 cm

= 7.4 cm

Since,

7.4 > 5.5,

XY + YZ > ZX

For the fourth the triangle

ΔMNS,

Here,

MN = 3 cm,

NS = 5 cm

MS = 3.4 cm

MN + NS

= 3 cm + 5 cm

= 8 cm

Since,

8 > 3.4,

MN + NS > MS

For the fifth triangle

ΔKLM,

We have

KL = 5.4 cm,

LM = 5 cm

KM = 2 cm

KL + LM

= 5.4 cm + 2 cm

= 7.4 cm

Since

7.4 cm > 5 cm,

KL + LM > KM

As, we have seen the sum of the length of two sides is greater than third side in each case. Thus, the given statement is false.
Correct option is 2.

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State true or false.Draw five triangles and measure their sides. Is in each case the sum of the length of any two sides is always less than the third side?

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State true or false.

Draw five triangles and measure their sides. Is in each case the sum of the length of any two sides is always less than the third side?