Question

Assertion : If the base and the altitude of a triangle are 4 cm and 8 cm respectively, then its area is 36 sq.cm Reason : Area of a triangle= 1/2 ×base × altitude


Both assertion and reason are true but reason is not the correct explanation of assertion.


Assertion is true but reason is false.

Both assertion and reason are true and reason is the correct explanation of assertion.


Assertion is false but reason is true.

Answer 1

Answer:

Base of a triangle is 4 cm longer than its altitude.

Area of triangle =48 cm2

Let base of triangle =b

Altitude =b−4

Area =21×b×h=48

21×b×(b−4)=48

b2−4b−96=0

(b−12)(b+8)=0

But, base cannot be negative

So, base =12 cm

Altitude=12−4=8 cm.

i hope my answer is correct any doubt you can ask me thank you

Answer 2

❒ Given :-

Assertion :

If the base and the altitude of a triangle are 4 cm and 8 cm respectively, then its area is 36 sq.cm .

Reason :

Area of a triangle= 1/2 ×base × altitude.

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❒ To Find :-

Which of the following is true :

i) Both assertion and reason are true but reason is not the correct explanation of assertion.

ii) Assertion is true but reason is false.

iii) Both assertion and reason are true and reason is the correct explanation of assertion.

iv) Assertion is false but reason is true.

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❒ Solution :-

${\large{\blue{\dashrightarrow{\red{\bf{Let's \: begin}}}}}}$

⇝First let's check the assertion :

✧ Here :

• ➳ Base = 4 cm
• ➳ Altitude = 8 cm
• ➳ Area = 36 cm²

⇝We know that :

${\large{\red{\bigstar{\purple{\boxed{\red{\boxed{\orange{\bf{Area = \frac{1}{2} \times Base \times Height}}}}}}}}}}$

⇝Area :

${\large{:{\twoheadrightarrow{\bf{ Area = \frac{1}{2} \times base \times Height}}}}}$

${\large{:{\twoheadrightarrow{\bf{ \: \: \: \: \: \: \: \: \: \: \frac{1}{2} \times 4 \times 8}}}}}$

${\large{:{\twoheadrightarrow{\bf{ \: \: \: \: \: \: \: \: \: \: \frac{1}{\cancel{2}} \times{\cancel{ 32}}}}}}}$

${\large{\purple{:{\longmapsto{\underline{\overline{\red{\boxed{\bf{Area = 16cm²}}}}}}}}}}$

❒ Conclusion :-

The area we found is 16 cm² .Hence, the assertion is false.

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⇝Checking the reason :

As mentioned above the formula for area of triangle :

${\large{\purple{:{\longmapsto{\underline{\overline{\red{\boxed{\bf{Area{\small_{(triangle)}} = \frac{1}{2} \times b \times h}}}}}}}}}}$

❒ Conclusion :-

Reason is true.

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❒ Final Conclusion :-

➻ Assertion is false but reason is true.

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