Question

2. In a AABC, in which Z A = 90°, AB = 4 cm and BC = 5 cm, the perimeter of A ABC is​

Answer 1

The Area of the triangle is 6 sq. cm.
Step-by-step explanation:
Given,
AB = 4 cm BC = 5 cm
∠A = 90°
We have dawn the triangle for your reference.
Since the triangle is right angled, so we use the Pythagoras Theorem to find the length of AC.
Pythagoras Theorem : The square of the hypotenuse is equal to the sum of square of perpendicular and square of base.
AB^2+AC^2=BC^2
On putting the values, we get;
4^2+AC^2=5^2\\\\16+AC^2=25\\\\AC^2=25-16=9\\\\
On taking square root on both side, we get;
\sqrt{AC^2}=\sqrt9\\\\AC=3\ cm
Now Area of the triangle is given by,
Area = \frac{1}{2}\times base\times height
Here base = AB = 4 cm
And height = AC = 3 cm
Area =\frac{1}{2}\times4\times3=2\times3=6\ cm^2
Hence The Area of the triangle is 6 sq. cm.