construct a right angled triangle MNO ,having hypotenuse ON = 60 mm and the sum of its base and its altitude = 55 mm.
Let x be the base length.
Let y be the altitude length.
x + y = 55 --> y = 55 - x ....eq1
x^2 + y^2 = 60^2....eq2
Sub eq1 into eq2:
x^2 + (55 -x)^2 = 60^2
Solve for x, and then use eq1 to solve for y.
To construct a right-angled triangle MNO with a hypotenuse ON = 60 mm and the sum of its base and altitude = 55 mm, follow these steps:
Step 1: Draw a line segment ON and mark its length as 60 mm.
Step 2: From point O, construct a perpendicular line segment OQ towards the right. This line will represent the base of the triangle. The length of OQ will be one side of the right angle.
Step 3: From point N, construct a perpendicular line segment NP downwards. This line will represent the altitude of the triangle. The length of NP will be the second side of the right angle.
Step 4: Measure the sum of the lengths of OQ and NP. Adjust the position of point Q and point P until the total length is equal to 55 mm.
Step 5: Mark the point M on line NP such that the length of MN is equal to the length of OQ. This will ensure that the triangle MNO is a right-angled triangle.
Step 6: Connect points M, N, and O to complete the triangle MNO.
Now you have constructed a right-angled triangle MNO with the given specifications.