Question

1)The semi perimeter of an isosceles triangle is 20 cm. If two of its equal sides are 15 cm each, then the third side is:


2)The semi perimeter of a triangle is 6 cm and the product of differences of semi perimeter and its respective sides(in cm) is 600. Then the area of the triangle is:

Answer 1

Answer:

Answer: third side=10cm

Step-by-step explanation:

Semi-perimeter=20cm

:. Perimeter=20x2=40cm

P=sum of all sides

→P=15+15+c(third side)

→40=30+c

→c=10cm←ans

(ii) S=semi-perimeter and a,b,c are sides of ∆

area of triangle, using heron's formula is

=> Area of ∆= √(s-a)(s-b)(s-c)

And product of differences of semi-perimeter and the sides is 600 i.e. (s-a)(s-b)(s-c) is given 600

:. area of ∆=√600

→A=10√6cm

Hope it helps

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Answer 2

Given:

Semi Perimeter of a triangle is 10 cm.

Two sides of triangle are 5 cm and 7 cm respectively.

To find:

The third side of the triangle.

Solution: Let the third side of the triangle be c cm and other sides be a is 5 cm and b is 7 cm respectively.

As we know that,

★ Semi perimeter = Sum of all sides (a + b + c)/2

⟹ S = 5 + 7 + c/2

⟹ 10 = 12 + c/2

⟹ c = 20 - 12

⟹ c = 8 cm ★

•°• Hence, the third side of the triangle is 8 cm.