the perimeter of a right triangle is 60 cm and its hypothense is 25 cm . Find the area of the triangle
Answers
Step-by-step explanation:
let, ∆ABC is a right angle triangle and B=90°
AB= x BC= y and AC=25
x+y+25=60
x+y=60-25 =35
By Pythagoras theorem
x^2+y^2=(25)^2
x^2+y^2 = 625
on squaring both side, we got
= ( x+y )^2 = (35)^2 = 1225
= (x+y)^2 = x^2+y^2+2xy
=1225 = 625 +2xy
=xy= 300
area of rectangle= 1/2base×height
1/2×300
=150
Answer:
perimeter of that triangle = 60 cm
the measure of hypothense = 25 cm
then the rest side measures = 60-25cm
=35cm
let one side be x
then the measure of third side must be = 35 - x
using pythagorean theorem
(25)^2 = (x)^2 +(35-x)^2
625 = x^2+x^2 -70x+1225
x^2+x^2 -70x +1225 -625 =0
2x^2 -70x+600=0
2x^2 -40x -30x +600=0
2x(x-20 ) -30 (x- 20) =0
(x-20) (2x - 30)=0
x-20=0
x=20
2x-30 = 0
2x = 30
x=15
so, one side measures 20cm and other 15 cm
If one side measures 20cm then other should measure = 35 - 20=15 cm
and if it measures 15 cm in other then should first measure as 35-15=20cm
one of them would be height and other would be base
so, the side as we find are 20 cm and 15 cm
formula of area of triangle =1/2 × base × height
1/2× 20 ×15 =150 cm ^2