The perimeter of a triangle is 60 cm. Its hypotenuse is 26 cm, find th

1.	The perimeter of a triangle is 60 cm. Its hypotenuse is 26 cm, find the otherand the area of the triangle.
Answer» Let a,b, c are the sides of a triangle . Given thathypotenuse(c) = 26 cm. a + b + c = 60 cm. ∴ a + b = 60 - c = 60 - 26 = ∴ a + b = 34 --------(1) In a right angled triangle c2= a^2+ b^2 a^2+ b^2= 262= 676 ---------(2) Now a^2+ ( 34 - a)^2= 676. [ from (1)] ⇒ a^²+ a^2- 68a + 1156 = 676 ⇒ 2a^2- 34a + 480 = 0 ⇒ a2- 17a + 240 = 0 ⇒ a^2- 10a - 24a + 240 = 0 ⇒ a(a - 10) - 24(a - 10) = 0 ∴ a = 10 , 24 but b = 34 - a then b = 24 , 10 ∴ sides of triangle are 10 , 24.

The perimeter of a triangle is 60 cm. Its hypotenuse is 26 cm, find the otherand the area of the triangle.

Answer»

Let a,b, c are the sides of a triangle .

Given thathypotenuse(c) = 26 cm.

a + b + c = 60 cm.

∴ a + b = 60 - c = 60 - 26 =

∴ a + b = 34 --------(1)

In a right angled triangle c2= a^2+ b^2

a^2+ b^2= 262= 676 ---------(2)

Now a^2+ ( 34 - a)^2= 676. [ from (1)]

⇒ a^²+ a^2- 68a + 1156 = 676

⇒ 2a^2- 34a + 480 = 0

⇒ a2- 17a + 240 = 0

⇒ a^2- 10a - 24a + 240 = 0

⇒ a(a - 10) - 24(a - 10) = 0

∴ a = 10 , 24

but b = 34 - a then b = 24 , 10

∴ sides of triangle are 10 , 24.