1) Simplify the following
a) √5 X √20 b)
2√10 + 3√10
5√2
2) Find the area of the triangle whose sides are 42cm , 34cm and
20cm . Also find the length of the longest altitude of the triangle .
3) Find rational numbers a and b so that 3 + √7
3− √7
= a + b √7
4) a) Simplify : 641/6
b) The base of a right triangle is 12cm and the hypotenuse is
15cm . Find its area .
5) Three similar coins were tossed simultaneously for 100 times and
the data recorded is as given below .
No. of heads 0 1 2 3
No. of tosses 22 30 28 20
Find the probability of a) two heads and one tail
b) Three heads and no tail c) at least one head
Answers
3+√7 / 3-√7
multiply 3+√7 on both numerator and denomerator
(3+√7)² / (3-√7)(3+√7) = a+b√7
⇒9 + 7 + 6√7 / 3² -√7² = a+b√7
⇒16+ 6√7 / 9-7 =a+b√7
⇒16+ 6√7 / 2 =a+b√7
⇒2(8+3√7)/2 =a+b√7
⇒8 +3√7 =a+b√7
on compairing both sides
a=8
b=3Answer:
Step-by-step explanation:
2.)make a trianlge ABC of 1 side=34cm one side=20 cm n the last side(base of the triangle) of 42cm
now use the heron's formula..according to the herons formula area of a triangle=under root [s(s-1st side of trianlge)(s-2nd side of triangle)(s-3rd side of trianle)].here s denotes the half of perimeter...perimeter is equals to the sum of all the sides of the triangle...that is 34+20+42 and it equals to 96..!!
S is half of the perimeter........here our perimeter is 96.........so its half is 48...!!!
now just put your values in the formula
under root[48(48-34)(48-20)(48-42)]
under root[48*6*14*28]
under root(112896)
=336 cm.
it is given in the question to find the height corresponding to the largest side...here the largest side is 42cm....so it means that we have to take 42cm as our base......now area of triangle is also 1/2(half)*base of the triangle*height of the triangle
A=1/2*B*H
336=1/2*42*H
336=21*H
H=336/21
H=16cm..!!
3.)3+√7 / 3-√7
multiply 3+√7 on both numerator and denomerator
(3+√7)² / (3-√7)(3+√7) = a+b√7
⇒9 + 7 + 6√7 / 3² -√7² = a+b√7
⇒16+ 6√7 / 9-7 =a+b√7
⇒16+ 6√7 / 2 =a+b√7
⇒2(8+3√7)/2 =a+b√7
⇒8 +3√7 =a+b√7
on compairing both sides
a=8
b=3
4.)
(a)641/6 = 106.83333 = 106 whole 5/6
for Q4 (b) please click on the link given above
(The area is 54 cm square i have found ab so please do the need full after this)