Question

The sides of a triangle are denoted by x,yand z. area of the triangle and perimeter of the triangle are denoted by P and q respectively. If P=
$\sqrt{q(q-x)(q-y)(q-z)}$
and x+y-z=y+z-x=z+x-y=4,then p is(in sq.units) is:
A)2✓3
B)3✓3
C)4✓3
D)6✓3

Answer 1

By seeing all given clues,

x + y - z + z + x - y = 8

2x = 8

x = 4 units

And,
x + y - z + y + z - x = 8

2y = 8

y = 4 units

Also given that,

z + x - y = 4

z + 4 - 4 = 4

z = 4 units

So we can say that this is an equilateral triangle.

Area of an equilateral triangle = [√3(side)²] /4

= √3 × 16 / 4

= 4 √3 units²

Hence the answer is C.

-WonderGirl

Answer 2

Answer:

4✓3

Step-by-step explanation:

By seeing all given clues,

x + y - z+z+ x - y = 8

2x = 8

x = 4 units

And,

x+y-z+y+z-x=8

2y = 8

y = 4 units

Also given that,

z + x - y = 4

z + 4 - 4 = 4

z = 4 units

So we can say that this is an equilateral

triangle.

Area of an equilateral triangle = [√3(side)] /4

= √3 x 16 / 4

= 4 √3 units²