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Standard X

Mathematics

Ratio of Area of Similar Triangles

In Δ DEW , AB...

Question

In $Δ D E W, A B | | E W$ . If AD = 4 cm, DE = 12 cm and DW = 24 cm, then find the value of DB.

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Solution

Let BD = x cm,

Then, $B W = (24 - x) c m$ and $A E = 12 - 4 = 8 c m$

In $Δ D E W, A B i s p a r a l l e l t o E W$

$∴ \frac{A D}{A E} = \frac{B D}{B W}$ [From Thales' Theorem]

$\Rightarrow \frac{4}{8} = \frac{x}{24 - x}$

$\Rightarrow 8 x = 96 - 4 x$

$\Rightarrow 12 x = 96$

$\Rightarrow x = \frac{96}{12} = 8$

$∴ D B = 8 c m$

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In a \Delta ABC, D and E are points on the sides AB and AC respectively such that DE||BC.
(i) If AD = 6cm, DB = 9 cm and AE = 8 cm, find AC.
(ii) If $\frac{A D}{D B} = \frac{3}{4}$ and AC = 15 cm, find AE.
(iii) If $\frac{A D}{D B} = \frac{2}{3}$ and AC = 18 cm, find AE.
(iv) If AD = 4, AE=8, DB =x-4, and EC = 3x - 19 find x
(v) If AD = 8 cm, AB=12 cm and AE = 12 cm, finde CE.
(vi) If ad = 4 CM, db = 4.5 cm and AE = 8 cm, find AC
(vii) If AD = 2 cm, AB = 6 cm and AC = 9cm, find AE.
(viii) If $\frac{A D}{B D} = \frac{4}{5}$ and 3C = 2.5 cm, find AE.
(ix) If AC=x, DB=x-2, AE=x+2 and EC=x-1, find the value of x.
(x) If AD= 8x -7. DB= 5x-3, AE=4x-3 and EC= (3x-1), find the value of x.
(xi) If AD= 4x-3, AE=8x -7, BC=3x-1 and CE=5x-3, find the value x.
(xii) If AD=2.5 cm, BD= =3.0 cm and AE=3.75 cm, find the length of AC.

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In ΔDEW, AB||EW. If AD = 4 cm, DE = 12 cm and DW = 24 cm, then find the value of DB.

Let BD = x cm, Then, BW=(24−x)cm and AE=12−4=8cm In ΔDEW, AB is parallel to EW ∴ ADAE=BDBW [From Thales' Theorem] ⇒ 48=x24−x ⇒ 8x=96−4x ⇒ 12x=96 ⇒ x=9612=8 ∴ DB=8cm

In $Δ D E W, A B | | E W$ . If AD = 4 cm, DE = 12 cm and DW = 24 cm, then find the value of DB.