Answer:

Step-by-step explanation:
We can use the Pythagorean theorem to find the length of the diagonal since drawing a diagonal across a rectangle results in two right angle triangles.
Length of diagonal
(The length of the diagonal can be thought of as the hypotenuse of one of the right angle triangles)


∴ The length of the diagonal is 
Hope this helps :)
Answer:

Step-by-step explanation:
Recall that the volume of a whole sphere is given by the formula:

then, the volume of a semi-sphere would be half of the formula above:

Now, the radius R is given by half of the semi-sphere diameter: 15/2 = 7.5 cm.
which makes our calculation:

Let's assume
Raj's age is x years
Zia's age is y years
we are given
Raj is three years older than zia
so, we get

now, we can solve for y

the sum of the squares of their ages is 369
so, we get

now, we can plug back y

now, we can solve for x





Since, age can not be negative
so, we will only consider positive

now, we can find y-value


So,
Raj's age is 15 years
Zia's age is 12 years...........Answer
Answer:
a) TO = OP = 13
b) Height = 12
Step-by-step explanation:
a) Isosceles triangle TOP with base TP = 10 cm, side TO = OP = x cm.
Perimeter of triangle TOP = 36 cm
=> TO + OP + TP = 36
=> x + x + 10 = 36
=> 2x = 26
=> x = 13
=> TO = OP = 13 cm.
b) Apply Pythagorean theorem:
height^2 + (base/2)^2 = side^2 (height^2 + (TP/2)^2 = TO^2)
or
height^2 + (10/2)^2 = 13^2
or
height^2 + 25 = 169
or
height^2 = 144
or
height = 12
Hope this helps!