Test: Problems on Pythagoras Theorem - CAT MCQ

Since monitors are measured along the diagonals this means we need to use pythagoras theorem for this right angled triangle.
H² = P² + B²
=17 * 17 + 21 * 21
  =289 + 441 = 730
H=27’’ (Approx)

Height of the triangle is the altitude. SInce the triangle is an isosceles triangle its median is equal to its altitude . So this means that the altitude is perpendicular and bisects the opposite side .
So BD=DC=26/2=13
So in right angled Triangle,
Using Pythagoras theorem,
H² = P² + B²
225 = P² + 169

a^2 + b^2 = c^2 ... pythagorean theorem

80^2 + 60^2 = c^2

6400 + 3600 = c^2

10,000 = c^2

c^2 = 10,000

c = sqrt(10,000)

c = 100

Sum of the length of the legs of a right angle triangle is 49
So let one leg be x, other will be 49-x
Applying Pythagoras theorem,
H²=P²+B²
41*41=x²+(49-x)²
1681=x² + 2401 + x² - 98x
2x²- 98x + 720 = 0
Dividing the equation by 2
x² - 49x + 360 = 0
x² - 9x - 40x + 360 = 0
x (x - 9) - 40 (x - 9) = 0
(x - 9)(x - 40) = 0
So x is either 9 or 40, 
So the smaller side is 9 cm
 

The height of wall will be the perpendicular for the right angle triangle. So applying pythagoras theorem
H²=P²+B²
11*11=P²+16
P=121-16=10.2 cm

Let width is x
Then length is x+1
Perimeter =x +x + x + 1 + x + 1 = 14
4 x= 12
x = 3
length = 4
Using Pythagoras theorem,
H² = P² + B²
=9 + 16 = 25
H = 5cm
An extra half meter on either side will give the length of the wire as 5 + 1 = 6cm