Question

The length of a side and corresponding height of a triangle are (x+2)cm and (7-x)cm write down a formula for the area A of the triangle in terms of x and show that A=7+5/2x-1/2x²

Answer 1

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Class 9

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>>Heron's Formula

>>Heron's Formula

>>The sides of a triangle are x, x + 1, 2x

Question

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The sides of a triangle are x,x+1,2x−1 and its area is x

10

. What is the value of x?

Medium

Solution

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If a,b,c are the sides of a triangle , then according to Hero's Formula area of triangle is

s(s−a)(s−b)(s−c)

where s=

2

a+b+c

For the given triangle,

s=

2

x+x+1+2x−1

=

2

4x

=2x

Area =x

10

2x(2x−x)(2x−x−1)(2x−2x+1)

=x

10

2x(x)(x−1)(1)

=x

10

x

2(x−1)

=x

10

2(x−1)

=

10

⇒2(x−1)=10

x−1=5

x=6