For an isosceles right-angled triangle having each of equal sides - a - we haveI- Area-12a2II- Perimeter -2-2 aIII- Hypotenuse -2 a Which of the following is true-a I onlyb II onlyc I and IId I and III

(c) I and II Area of triangle = 12 #215;Base #215;Height=12 #215;a #215;a=12a2 Hypotenuse = a2+a2=2a2=2a Perimeter = a+a+2a=2a+2a=a(2+2) ...

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Area of an Equilateral Triangle

For an isosce...

Question

For an isosceles right-angled triangle having each of equal sides 'a', we have
I. $Area = \frac{1}{2} a^{2}$
II. $Perimeter = (2 + \sqrt{2}) a$
III. Hypotenuse = 2a
Which of the following is true?
(a) I only
(b) II only
(c) I and II
(d) I and III

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Solution

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Area = \frac{b \cdot \sqrt{4 a^{2} - b^{2}}}{4}

Height = \frac{1}{2} \sqrt{4 a^{2} - b^{2}}

Question 5

In an isosceles triangle, one angle is $70^{\circ}$ . The other two angles are of

i) $55^{\circ}$ and $55^{\circ}$
ii) $70^{\circ}$ and $40^{\circ}$
iii) Any measure

In the given option(s) which of the above statement(s) are true?

a) (i) only
b) (ii) only
c) (iii) only
d) (i) and (ii)

(1 + \sqrt{2}) a

(2 + \sqrt{2}) a

3 a

(3 + \sqrt{2}) a

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