SChand Composite Mathematics Class 7 Chapter 11 Triangle and it's Properties Exercise 11D

 Exercise 11 D 

Question 1

Find each of these , find the area of the shaded square: 

(i) (diagram to be added)

Sol: $A=36+64$

$A=100 \mathrm{~cm}^{2}$

(ii)  (diagram to be added)

Sol: $A=34+47$

$A=81 \mathrm{~cm}^{2}$

(iii)  (diagram to be added)

Sol: $A=3.42+2.25$

$A=5.67 \mathrm{~cm}^{2}$

Question 2

There squares have areas equal to $27 \mathrm{~cm}^{2}, 12 \mathrm{~cm}^{2}$ and $15 \mathrm{~cm}^{2}$

(i) Will the squares exactly surround a right angles triangle? 

(ii) Explain your answer.

Ans: Yes because $H^{2}=B^{2}+P^{2} \Rightarrow 27=12+15$

Question 3

State an equation that can be used to find the missing length for each triangle. 

(i) (Diagram to be added)

Ans: $x^{2}=4^{2}+7^{2}$

(ii)  (Diagram to be added)

Ans: $a^{2}=5^{2}+5^{2}$

(iii)  (Diagram to be added)

Ans: $p^{2}=13^{2}-7^{2}$

(iv)  (Diagram to be added)

Ans: $y^{2}=10^{2}-3^{2}$

Question 4

Two sides being given, calculate the third side marked by a letter in each right angled triangle> 

(i)   (Diagram to be added)

Sol: $b^{2}=15^{2}+8^{2}$

$b^{2}=225+64$

$b^{2}=289$

$b=17$

(ii)  (Diagram to be added)

Sol: $c^{2}=12^{2}+5^{2}$

$c^{2}=144+25$

$c^{2}=169$

$c=13$

(iii)   (Diagram to be added)

Sol: $2 a^{2}=21^{2}+d^{2}$

$d^{2}=2 g^{2}-21^{2}$

$d^{2}=841-441$

$d^{2}=400$

d= 20 answer 

(iv) (Diagram to be added)

Sol: $15^{2}=9^{2}+x^{2}$

$x^{2}=15^{2}-9^{2}$

$x^{2}=225-81$

$x^{2}=144$

$x=12$

Question 5

What is the length of the diagonal of the rectangle? 

(diagram to be added)

Sol: $H^{2}=P^{2}+B^{2}$

$H^{2}=6^{2}+8^{2}$

$H^{2}=36+64$

$H^{2}=100 \Rightarrow H=10$

Question 6

Calculate.

(diagram to be added)

Sol:  $\Rightarrow H^{2}=P^{2}+B^{2}$

$\Rightarrow B^{2}=H^{2}-P^{2} \Rightarrow B^{2}=15^{2}-12^{2}$

$\Rightarrow B^{2}=225-144$

$\Rightarrow B^{2}=81 \Rightarrow B=9$

$H=2 \times B=2 \times 9$ H= 18 ANSWER 

Question 7

Calculate the length of : 

(i) BD 

(ii) BC 

(DIAGRAM TO BE ADDED)

(i) 

$\begin{aligned} P^{2} &=H^{2}-B^{2} \\ &=10^{2}-6^{2} \quad \Rightarrow \quad P^{2}=100-36 \\ P^{2} &=64 \\ P &=B D=8 \end{aligned}$

(ii) 

$\begin{aligned} H^{2} &=P^{2}+B^{2} \\ &=8^{2}+15^{2} \\ &=64+225 \\ &=289 \\ H &=B C=17 \end{aligned}$

Question 8

Your garden is in the shape of a rectangle that measures 24 m by 32 m . You want to put a diagonal walk from corner to corner across the garden. What will be the length of the walk ? 

(DIAGRAM TO BE ADDED)

Sol:  

$\begin{aligned} H^{2} &=P^{2}+B^{2} \\ H^{2} &=24^{2}+32^{2} \\ &=576+1024 \\ H^{2} &=1600 \\ H &=40 m \text { Ans } \end{aligned}$

Question 9

A tree is broken at a height of 8 m from the ground and its top touches the ground at a distance of 15m from the base of the tree. Find the original height of the tree. 

(DIAGRAM TO BE ADDED)

Sol: 

$\begin{aligned} H^{2} &=B^{2}+p^{2} \\ &=15^{2}+8^{2} \\ &=225+64 \\ H^{2} &=289 \end{aligned}$

$H=17 \mathrm{~m}$

Original height of the tree= 8 + 17 = 25 m answer 

Question 10

To find the distance from point A to point B on opposite ends of a lake ,a  figures as shown. How far is it it from A to B? 

(DIAGRAM TO BE ADDED)

Sol: 

$\begin{aligned} H^{2} &=p^{2}+B^{2} \\ &=16^{2}+12^{2} \\ H^{2} &=256+144 \\ H^{2} &=400 \\ H &=20 m \end{aligned}$