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Standard VII

Mathematics

Construction of an Isosceles Triangle Triangle

In the figure...

Question

In the figure, $A P = 3 c m, A R = 4.5 c m, A Q = 6 c m, A B = 5 c m$ , and $A C = 10 c m$ . Find the length (in cm) of $A D$

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Solution

$Δ A P Q$ is similar to $Δ A B C$
( $A A A$ postulate)
$(∵) \frac{A P}{A B} = \frac{A Q}{A C}$
As $A D$ is line from common vertex,
$Δ A P R \sim Δ A B D$
$\frac{A P}{A B} = \frac{A R}{A D}$
$∴ A D = \frac{A B \times A R}{A P}$
$= \frac{5 \times 4.5}{3}$
$= 7.5 C M$

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Similar questions

Q. In the given figure

P

and

Q

are points on sides

A B

and

A C

respectively of

△ A B C .

A P = 3 c m, P B = 6 c m, A Q = 5 c m

and

Q C = 10 c m,

show that

B C = 3 P Q .

Q. In given figure,

P

and

Q

are points on the sides

A B

and

A C

respectively of

△ A B C

such that

A P = 3.5 c m, P B = 7 c m, A Q = 3 c m

and

Q C = 6 c m

. If

P Q = 4.5 c m

, find

B C

Q. In figure 1, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then the length of AP (in cm) is
(a) 7.5
(b) 15
(c) 10
(d) 9

In a $Δ A B C$ , AD is the bisector of $∠ A$ , meeting side BC at D.
(i) If BD= 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD= 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB= 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB =10 cm, AC =14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.
(vi) If AD= 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AB= 3.6 cm, BC e 6 cm and BD = 32 cm, find AC.
(viii) If AB =10 cm, AC = 6 cm and BC = 12 cm, find BD and DC

In the figure given below AB, CD, and EF are parallel lines. Given AB = 9 cm, DC = y cm, EF = 4.5 cm, BC = x cm, and CE = 3 cm. The value of 'x' and 'y' are:

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In the figure, AP=3 cm,AR=4.5 cm,AQ=6 cm,AB=5 cm, and AC=10 cm. Find the length (in cm) of AD

ΔAPQ is similar to ΔABC(AAA postulate)(∵)APAB=AQACAs AD is line from common vertex,ΔAPR∼ΔABDAPAB=ARAD∴AD=AB×ARAP=5×4.53=7.5CM

In the figure, $A P = 3 c m, A R = 4.5 c m, A Q = 6 c m, A B = 5 c m$ , and $A C = 10 c m$ . Find the length (in cm) of $A D$

$Δ A P Q$ is similar to $Δ A B C$
( $A A A$ postulate)
$(∵) \frac{A P}{A B} = \frac{A Q}{A C}$
As $A D$ is line from common vertex,
$Δ A P R \sim Δ A B D$
$\frac{A P}{A B} = \frac{A R}{A D}$
$∴ A D = \frac{A B \times A R}{A P}$
$= \frac{5 \times 4.5}{3}$
$= 7.5 C M$