Question

Is it possible to construct triangles with measures as given below?

(i) ΔDEF with DE = 3 cm, EF = 30 cm, DF = 32 cm
(ii) ΔPQR with PQ = 30 cm, QR = 2 cm, PR = 20 cm

Answer 1

Answer:

rule to know

if it is sum

sum of two sides should be greater than third side all cases

first question following

30+3>32

33>32

so it forms a triangle

2) it's not going to form

because 20+2<30

22<30

so it's not going to form

rule two : if we know diff

any two sides difference should be less than the third side

Answer 2

Step-by-step explanation:

Given:-

i) ΔDEF with DE = 3 cm, EF = 30 cm, DF = 32 cm

(ii) ΔPQR with PQ = 30 cm, QR = 2 cm, PR = 20 cm

To find:-

Is it possible to construct triangles with measures as given below?

(i) ΔDEF with DE = 3 cm, EF = 30 cm, DF = 32 cm

(ii) ΔPQR with PQ = 30 cm, QR = 2 cm, PR = 20 cm

Solution:-

(i) ΔDEF with DE = 3 cm, EF = 30 cm, DF = 32 cm

we know that the sum of any two sides is greater than the third side.

1)DE+EF=3+30=33cm

DE+EF>DF

2)DE+DF=3+32=35cm

DE+DF>EF

3)DF+EF=30+32=62cm

DF+EF>DE

and The difference of any two sides is less than the third side

4)EF-DE=30-3=27cm

EF-DE<DF

5)DF-DE=32-3=29cm

DF-DE<EF

6)DF-EF=32-30=2cm

DF-EF<DE

The given measurements follows the above inequalities,so it is possible to construct a triangle with the measurements.

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ii) ΔPQR with PQ = 30 cm, QR = 2 cm, PR = 20 cm

we know that the sum of any two sides is greater than the third side.

1)PQ+QR=30+2=32 cm

PQ+QR>PR

2)QR+PR=2+20=22cm

QR+PR<PQ

The given measurements does not follow the inequality,so it is not possible to construct a triangle with the given measurements.

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Inequalities of a triangle:-

• The sum of any two sides is greater than the third side.
• The difference between any two sides is less than the third side.

Verified ✅