Practice Set 1.1 Similarity Class 10th Mathematics Part 2 MHB Solution

Practice Set 1.1
  1. Base of a triangle is 9 and height is 5. Base of another triangle is 10 and height is…
  2. If figure 1.13 BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8, then find a (deltaabc)/a (deltaadb)…
  3. In adjoining figure 1.14 seg PS seg RQ , seg QT seg PR. If RQ = 6, PS = 6 and PR = 12,…
  4. In adjoining figure, AP ⊥ BC, AD || BC, then find A(ΔABC) : A (ΔBCD) n…
  5. In adjoining figure PQ BC, AD BC then find following ratios. (i) a (deltapqb)/a…

Practice Set 1.1
Question 1.

Base of a triangle is 9 and height is 5. Base of another triangle is 10 and height is 6. Find the ratio of areas of these triangles.


Answer:

We know that area of triangle =  × Base× Height

⇒ Area (triangle 1) =  ×9× 5


⇒ Area (triangle 2) =  ×10× 6


= 30


∴ the ratio of areas of these triangles will be = 





Question 2.

If figure 1.13 BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8, then find 



Answer:

Here,ΔABC and ΔADB has common Base.

∴ 


(PROPERTY: Areas of triangles with equal bases are proportional to their corresponding heights.)


⇒ 





Question 3.

In adjoining figure 1.14 seg PS ⊥ seg RQ , seg QT ⊥ seg PR. If RQ = 6, PS = 6 and PR = 12, then find QT.


Answer:



Considering, Area of (ΔPQR) with base QR

⇒ PS will be the Height


Now, consider the Area of (ΔPQR) with base PR


⇒ QT will be the Height


∵ , the triangle is the same


⇒ the area will be the same irrespective of the base taken.


And we know that area of triangle =  × Base× Height


⇒ ×QR×PS

×PR×QT


⇒ ×6×6


×12×QT


⇒ QT = 3


Question 4.

In adjoining figure, AP ⊥ BC, AD || BC, then find A(ΔABC) : A (ΔBCD)



Answer:


We can re-draw the fig.1.15(as shown above) where we add DO


which will be height of ΔBCD.


Now, 


(PROPERTY: Areas of triangles with equal bases are proportional to their corresponding heights.)



⇒ 


(∵ the distance between the two parallel lines is always equal ⇒ AP = DO)


 = 1:1



Question 5.

In adjoining figure PQ ⊥ BC, AD ⊥ BC then find following ratios.


(i) 

(ii) 

(iii) 

(iv) 


Answer:

We know that area of triangle =  × Base× Height

(i)


(PROPERTY:Areas of triangles with equal heights are proportional to their corresponding bases.)


(ii)


(PROPERTY: Areas of triangles with equal bases are proportional to their corresponding heights.)


(iii)


(PROPERTY:Areas of triangles with equal heights are proportional to their corresponding bases.)


(iv)



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