Question

Q. The base of a right angled triangle is 12 cm and its hypotenuse is 13 cm long. Find its area and the perimeter.

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Answer 1

Answer:

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It is given that

ABC is a right angled triangle

BC = 12 cm

AB = 13 cm

• Using the Pythagoras theorem

AB²= AC² + BC²

Substituting the values

13² = AC² + 12²

AC²= 13² – 12²

So,

AC²= 169 – 144 = 25

AC = √25 = 5 cm

We know that

Area of triangle ABC = ½ × base × height

Substituting the values

= ½ × 12 × 5

= 30 cm²

Similarly,

Perimeter of triangle ABC = AB + BC + CA

Substituting the values

= 13 + 12 + 5

= 30 cm

thus the required perimeter and area is 30cm and 30cm²

Answer 2

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Base = 12cm

Hypotenuse = 13 cm

Height = ?

${b}^{2} + {h}^{2} = hypotenuse ^{2}$

12^2 + h^2 = 13 ^2

144 + h^2 = 169

h^2 =169 -144

h^2 = 25

h=5

Area = 1/2 × base ×height = 1/2 ×12×5 = 30cm^2

Perimeter = 12 +13 +5 =30 cm

• Hope it helps ✔