Q. 135.0( 1 Vote )

# A roof has a cross section as shown in the diagram,

(i) Identify the similar triangles

(ii) Find the height h of the roof.

Answer :

In ΔYZW

Let ∠YZW = x

⇒ ∠ZYW = 90-x (∵ It is a right-angled triangle)

⇒ ∠XYW = x (∵ ∠ZYX is 90)

⇒ ∠YZW = ∠XYW ----(1)

Similarly,

∠XYW = ∠XZY ----(2)

Now,

In ΔYWZ and ΔXYZ

∠WXY = ∠ZXY (common)

∠YWZ = ∠XYZ (by (1))

∴ ΔYWZ ∼ ΔXYZ ----(3)

Now,

In ΔXWY and ΔXYZ

∠YXW = ∠ZXY (common)

∠XYW = ∠XZY (by (2))

∴ ΔXWY ∼ ΔXYZ ----(4)

⇒ ΔXWY ∼ ΔXYZ ∼ ΔYWZ (by (3) and (4))

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