Question

The lateral sides of an isosceles triangle with vertex angle 90° are 12cm each. Find
the area of the triangle and hence its base.
​

Answer 1

Answer:

Since the sum of the interior angles of any triangle adds up to

180

∘

and also the base angles of an isosceles triangle are equal,we may let the base angles be

x

, then the vertex angle is

2

x

.

∴

x

+

x

+

2

x

=

180

∘

.

∴

x

=

45

∘

.

Therefore the vertex angle is

90

Step-by-step explanation:

An isosceles triangle has two sides of equal length. Likewise, the opposite angles of the sides are the same

So lets assume each angle be

x

and the bigger angle be

2

x

(since it is twice the base angle)

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Now, we know that sum of the angles in a triangle is 180 degree

So,

→

2

x

+

x

+

x

=

180

∘

→

4

x

=

180

∘

→

x

=

180

4

⇒

x

=

45

∘

Now the other angle is

2

x

which is

45

×

2

=

90

∘

Hope this helps!!! ☺☻ have a good day..