Question

RHP ∼ ∆NED and HP : ED = 4 : 5, then .... .

1) ∆RHP is a bigger triangle.
2) ∆RHP is a smaller triangle.
3) Both the triangles are congruent.
4) Cannot be decided.​

Answer 1

Solution :-

we know that,

• when two ∆'s are similar , they have same shape but not always same size .

given that,

→ RHP ∼ ∆NED

So,

→ RH/NE = HP/ED = RP/ND = 4/5 (given)

as we can see that, ,

→ RH < NE

→ HP < ED

→ RP < ND

since sides of ∆NED are greater than ∆RHP .

Therefore, we can conclude that, side of ∆NED are greater .

Hence, we can conclude that, (2) ∆RHP is a smaller triangle.

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Answer 2

Answer:

The sides of △RHP will be 5/4

times the sides of △NED

∴RH= 5/4 ×NE= 5/4

×7=8.75 cm

∠H=∠E=30 ∘

∠R=∠N=20 ∘

Construction:

Step 1: Draw base RH=8.75 cm with a ruler.

Step 2: Draw a line at an angle of 30 ∘

from point H.

Step 3: Draw a line at an angle of 20 ∘

from point R.

Step 4: Mark the intersection point of the lines in steps 2 and 3 as point P and draw lines joining P−R and P−H.

△RHP is the required triangle.