Question

find the area of triangle ABC when <A=<C=45, <B=90 and AC =20root2cm

Answer 1

Since it is a right angled triangle ,we can apply Pythagoras theorem.
Angle A = Angle C = 45°

So according to isosceles triangle property,
AB = BC
AC^2 = AB^2 + BC^2
(20✓2)^2 = 2(AB)^2
800 = 2AB^2
AB = √400
AB = 20 cm

AB = BC = 20 cm

Now AB and BC are the base and altitude of the given triangle.

We know,
Area of triangle = 1/2 ( Base x Altitude)
= 1/2 x 20 x 20
= 200 cm^2

Hope This Helps You!

Answer 2

As one of the angles of the triangle is 90°,it is a right angled triangle.
Therefore, its area = 1/2(BC)(AB)
Given ∠A=∠C=45° and AC=20√2 cm.
Tan C=AB/BC
⇒Tan 45°= AB/BC
⇒1=AB/BC
⇒AB=BC.----(1)
By Pythagoras theorem, (AB)²+(BC)²=(AC)²
⇒(AC)²=(AB)²+(AB)²
⇒(AC)²=2(AB)²
⇒(AB)²= [(20√2)²/2]
⇒(AB)²=400
⇒AB=√400
⇒AB=20 cm
Therefore, AB=BC= 20 cm (from (1))
Hence, area of ΔABC=(1/2)(BC)(AB)
=(1/2)(20)(20)
=200 cm²
∴ The area of the given triangle is 200 cm²