Question

find the area between the line y=x,x axis and the ordinate at x=5.

Answer 1

its simple, x is a horizontal line, x = 5 is a vertical line and y = x is a line inclined at 45 degree with horizontal and vertical. so these three lines form a right angle triangle. Here the base is 5 and angle is 45 degree. now tan 45 = perpendicular /5 therefore perpendicular = 5 (tan 45), so perpendicular (height) = 5

now area of triangle = (1/2) x base x height
= 1/2 x 5 x 5
= 5 sq. unit

Answer 2

from "perpendicular (height)" i mean perpendicular i.e height and from "x is a horizontal line" i mean x axis is a horizontal line.

there are other ways to solve this question. like to find intersection of line y =x and and x = 5, which will give (5, 5) then solve it by the method of triangle (as i explained above or by a formula (which i don't remember, but you can check in your text book)

Answer 3

i checked it the answer is 25/2sq.units and i cant found the answer in my solution