Construct a right triangle whose base is 12cm and sum of its hypotenuse and other side is 18cm

Answer 1

other side = x
hypotenuse = √(x^2 + 12^2)

x + √(x^2 + 144) = 18
√(x^2 + 144) = 18-x
square both sides:
x^2 + 144 = 324 - 36x + x^2
36x = 324-144
x = 5

your triangle is 5 by 12 with a hypotenuse of 13

check:
is 5+13 = 18? YUP
is 5^2 + 12^2 = 13^2 ? , YUP

you should recognize triangles such as 3,4,5 and 5,12,13 as right-angled.
They are the simplest of such triangles with whole numbers.
(note that 6,8,10 is also such a triangle but it is similar to 3,4,5)