The difference between the two adjoining sides containing right angle of a right-angled
triangle is 14 cm. The area of triangle is 120 cm2
. Verify this area by using Heron’s formula
Answers
YOUR ANSWER IN THE FOLLOWING STEPS-:::::
Let the perpendicular be a cm
Base = a+14 cm
According to question
Area = 120
1/2 b *p =120
a(a+14) = 240
a^2 +14a-240 = 0
a^2 +24a - 10a - 240=0
a(a+24) - 10(a+24)= 0
(a+24)(a-10)=0
a= - 24 and a=10
Neglecting negative value, we get
a=10
Perpendicular = 10 cm
Base = 24 cm
Hypotenuse = 25 cm
Now,
semi perimeter = 59/2
(s-a) = 39/2
(s-b) = 11/2
(s-c) = 9/2
Area of triangle = root( 59*39*11*9/16)
= 3/4 * root 59*39*11
= 3/4 * 160(approx.)
= 3*40
=120 cm sq.
Answer:
Let the perpendicular be a cm
Base = a+14 cm
According to question
Area = 120
1/2 b *p =120
a(a+14) = 240
a^2 +14a-240 = 0
a^2 +24a - 10a - 240=0
a(a+24) - 10(a+24)= 0
(a+24)(a-10)=0
a= - 24 and a=10
Neglecting negative value, we get
a=10
Perpendicular = 10 cm
Base = 24 cm
Hypotenuse = 25 cm
Now,
semi perimeter = 59/2
(s-a) = 39/2
(s-b) = 11/2
(s-c) = 9/2
Area of triangle = root( 59*39*11*9/16)
= 3/4 * root 59*39*11
= 3/4 * 160(approx.)
= 3*40
=120 cm sq.