At 11a.m., a two - metre high pole gives a shadow of 2.5 m.A tall tree in the same area at the same time gives a shadow of 17.5 m. What is the height of the tree?
Answers
Given :
A pole of height 2 m which casts a shadow of 2.5 m.
And a tree whose height is not given but casts a shadow of 17.5 m.
Find :
Height of the tree.
Solution :
Assume two triangles ABC and PQR such that,
AB = 2 m, BC = 2.5 m and QR = 17.5 m
Δ ABC for pole and ΔPQR for tree.
Let PQ = x (height of tree)
Now,
In ΔABC
→ Height : Shadow
→ 2 : 2.5 _____ (eq 1)
Similarly, In ΔPQR
→ Height : Shadow
→ x : 17.5 ____ (eq 2)
From (eq 1) and (eq 2) we have,
→ Height : Shadow
→ 2 : 2.5
→ x : 17.5
Cross multiply them
→ 2 × 17.5 = x × 2.5
→ 35 = 2.5x
→ x = 35/2.5
→ x = 14
∴ Height of tree is 14 m.
______________________________
✯ Verification :
From above calculations we have x = 14.
So,
→ Height : Shadow
→ 2 : 2.5
→ 14 : 17.5
Cross multiply them
→ 2 × 17.5 = 2.5 × 14
→ 35 = 35
Pole's height = 2 m and Tree's height = ?
Shadow of pole = 2.5 and that of tree = 17.5
Height : Shadow
2 : 2.5
x : 17.5
On solving we get x = 14