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Find the height of the given triangle if its base is 26 inches and the slant side is 15 inches long as shown below.
Detailed Solution for Test: Problems on Pythagoras Theorem - Question 3
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 in right angled Triangle,
Using Pythagoras theorem,
H2 = P2 + B2
225 = P2 + 169
If the sum of the squares of a and b is the same as the square of c and if m < n, then for what value of k can the Pythagorean triples be generated with the following equations?
a = n2 + k , b = 2mn : c = m2 + n2
If the sum of the length of the legs of a right triangle is 49 cm and the hypotenuse is 41 cm, find its shortest side.
Detailed Solution for Test: Problems on Pythagoras Theorem - Question 7
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,
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
A wood frame for pouring concrete has an interior perimeter of 14 metres. Its length is one metre greater than its width. The frame is to be braced with twelve-gauge steel cross-wires. Assuming an extra half-metre of wire is used at either end of a cross-wire for anchoring, what length of wire should be cut for each brace?
Detailed Solution for Test: Problems on Pythagoras Theorem - Question 9
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
Test: Problems on Pythagoras Theorem - Question 10
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