Question 13 Marks
A ladder 13 m long rests against a vertical wall. If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from the ground.
Answer
View full question & answer→12 m
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Question 23 Marks
Length of the sides of triangles are given. Determine which of them is a right angled triangle. In case of right angled triangle determine the hypotences
(i) 5 cm, 4 cm, 3 cm
(ii) 10 cm, 15 cm, 13 cm
(iii) 80 cm.
(i) 5 cm, 4 cm, 3 cm
(ii) 10 cm, 15 cm, 13 cm
(iii) 80 cm.
Answer
View full question & answer→(i) yes, hypotenuse = 5cm
(ii) no,
(iii) yes, hypotenuse = 100 cm
(ii) no,
(iii) yes, hypotenuse = 100 cm
Question 33 Marks
In $\triangle ABC$, if $AB = AC$ and D is a point on BC .
Prove that $AB ^2- AD ^2= BD \quad CD$.
Prove that $AB ^2- AD ^2= BD \quad CD$.
Answer
View full question & answer→[Hint. Draw $A E \perp B C$. Then $\triangle A E B \cong \triangle A E C$.
$\therefore B E=E C .$
Now, $A B^2=A E^2+B E^2$ and $A D^2=A E^2+D E^2$.
$\begin{aligned}\therefore A B^2-A D^2 & =B E^2-D E^2 \\& =(B E+D E)(B E-D E) \\& =(C E+D E) \quad B D \\& =C D \quad B D=B D \quad C D]\end{aligned}$
$\therefore B E=E C .$
Now, $A B^2=A E^2+B E^2$ and $A D^2=A E^2+D E^2$.
$\begin{aligned}\therefore A B^2-A D^2 & =B E^2-D E^2 \\& =(B E+D E)(B E-D E) \\& =(C E+D E) \quad B D \\& =C D \quad B D=B D \quad C D]\end{aligned}$
Question 43 Marks
From the given figure, find the area of trapezium ABCD.
Answer
View full question & answer→$14 cm^2$
[Hint. Area of trapezium $=\frac{1}{2} \times$ (sum of parallel sides) $\times$ (distance between them).]
[Hint. Area of trapezium $=\frac{1}{2} \times$ (sum of parallel sides) $\times$ (distance between them).]
Question 53 Marks
In $\triangle A B C, \angle C=90$.
If $B C=a, A C=b$ and $A B=c$, find :
(i) $c$ when $a=8 cm$ and $b=6 cm$.
(ii) $a$ when $c=25 cm$ and $b=7 cm$
(iii) $b$ when $c=13 cm$ and $a=5 cm$.
If $B C=a, A C=b$ and $A B=c$, find :
(i) $c$ when $a=8 cm$ and $b=6 cm$.
(ii) $a$ when $c=25 cm$ and $b=7 cm$
(iii) $b$ when $c=13 cm$ and $a=5 cm$.
Answer
View full question & answer→(i) c = 10cm
(ii) a = 24cm
(iii) b = 12cm
(ii) a = 24cm
(iii) b = 12cm
Question 63 Marks
In $\triangle A B C$, if $A B=A C$ and $D$ is a point on $B C$.
Prove that $AB ^2- AD ^2= BD \times CD$.
Prove that $AB ^2- AD ^2= BD \times CD$.
Answer
View full question & answer→self
Question 73 Marks
A ladder 13 m long rests against a vertical wall. If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from the ground.
Answer
View full question & answer→12 m
Question 83 Marks
A ladder 17 m long reaches the window of a building 15 m above the ground. Find the distance of the foot of the ladder from the building.
Answer
View full question & answer→8 m
Question 93 Marks
Length of the sides of triangles are given. Determine which of them is a right angled triangle. In case of right angled triangle determine the hypotences
(i) $5 cm, 4 cm, 3 cm$
(ii) $10 cm, 15 cm, 13 cm$
(iii) 80 cm ,
(i) $5 cm, 4 cm, 3 cm$
(ii) $10 cm, 15 cm, 13 cm$
(iii) 80 cm ,
Answer
View full question & answer→(i) yes, hypotenuse =5 cm
(ii) no ,
(iii) yes, hypotenuse $=100 cm$
(ii) no ,
(iii) yes, hypotenuse $=100 cm$
Question 103 Marks
In $\triangle A B C, \angle C=90^{\circ}$.
If $B C=a, A C=b$ and $A B=c$, find:
(i) $c$ when $a=8 cm$ and $b=6 cm$.
(ii) $a$ when $c=25 cm$ and $b=7 cm$
(iii) $b$ when $c=13 cm$ and $a=5 cm$
If $B C=a, A C=b$ and $A B=c$, find:
(i) $c$ when $a=8 cm$ and $b=6 cm$.
(ii) $a$ when $c=25 cm$ and $b=7 cm$
(iii) $b$ when $c=13 cm$ and $a=5 cm$
Answer
View full question & answer→(i) $c=10 cm$
(ii) $a=24 cm$
(iii) $b=12 cm$
(ii) $a=24 cm$
(iii) $b=12 cm$