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