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The base of a right angled triangle is 5 metres and hypotenuse is 13 metres. Its area will be:
- a)25 m2
- b)28 m2
- c)30 m2
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The base of a right angled triangle is 5 metres and hypotenuse is 13 m...
Solution:
Given, base = 5m and hypotenuse = 13m
Let height be h.
Using Pythagoras theorem, we have:
$$(\text{hypotenuse})^2 = (\text{base})^2 + (\text{height})^2$$
$$(13)^2 = (5)^2 + h^2$$
$$h^2 = 169 - 25$$
$$h^2 = 144$$
$$h = 12 \text{m}$$
Therefore, the height of the triangle is 12m.
Area of the triangle = 1/2 × (base) × (height)
$$\text{Area} = \frac{1}{2} \times 5 \times 12$$
$$\text{Area} = 30 \text{m}^2$$
Hence, the area of the triangle is 30 m². Therefore, the correct option is (c).
Given, base = 5m and hypotenuse = 13m
Let height be h.
Using Pythagoras theorem, we have:
$$(\text{hypotenuse})^2 = (\text{base})^2 + (\text{height})^2$$
$$(13)^2 = (5)^2 + h^2$$
$$h^2 = 169 - 25$$
$$h^2 = 144$$
$$h = 12 \text{m}$$
Therefore, the height of the triangle is 12m.
Area of the triangle = 1/2 × (base) × (height)
$$\text{Area} = \frac{1}{2} \times 5 \times 12$$
$$\text{Area} = 30 \text{m}^2$$
Hence, the area of the triangle is 30 m². Therefore, the correct option is (c).
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Community Answer
The base of a right angled triangle is 5 metres and hypotenuse is 13 m...
Hypotenuse = √(base2+height2)
height2 = Hypotenuse2 - base2
height = √(132 - 52)
⇒ √144 ⇒ 12
height2 = Hypotenuse2 - base2
height = √(132 - 52)
⇒ √144 ⇒ 12
Area of the triangle = 1/2(base*height)
=1/2(5 x 12 ) m2
= 30m2
=1/2(5 x 12 ) m2
= 30m2
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