Question

find the area of triangle two side of which are 10cm and 12cm and the Perimeter is 32 cm​

Answer 1

Solution:-

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$\implies$ Here, the question has given us the two sides of a triangle that are 10 cm and 12 cm respectively. The question has also given us the perimeter of the triangle that is 32 cm respectively. We will find the 3rd side by applying the formula of perimeter of triangle by assuming the 3rd side as x and after it by applying the Heron's formula we will get the area of the triangle.

ANSWER:-

◦ 3rd side of the triangle is 10 cm.

◦ Area of the triangle is 48 cm².

GIVEN:-

⟶ 1st side = 10 cm

⟶ 2nd side = 12 cm

⟶ Perimeter = 32 cm

TO FIND:-

⇒ 3rd side = ?

⇒ Area = ?

FORMULA:-

⟿ Perimeter = a + b + c [For finding 3rd side]

⟿ Area:- √[s(s - a)(s - b)(s - c)]

We will get the area of the triangle by Heron's Formula:-

1. First of all we hav to find the semiperimeter of the triangle = Perimeter / 2 = s
2. Secondly, we have to take the square root of the product of the semiperimeter of the triangle with the difference of the sides of triangle and semiperimeter with them.

SOLVING BY APPLYING THE FORMULA:-

• Finding the 3rd side:-
• Let 3rd side be x.

⟾ 32 = 10 + 12 + x

⟾ 32 = 22 + x

⟾ Taking 22 to L.H.S.

⟾ 32 - 22 = x

⟾ 10 = x

⟾ x = 10 cm

Thus, 3rd side is 10 cm.

• Finding the area:-

⟾ Area = √[16(16 - 10)(16 - 10)(16 - 12)]

⟾ Area = √16 × 6 × 6 × 4

⟾ Area = √16 × 144

⟾ Area = √16 × 144 = √2304

⟾ Area = √2304

⟾ Area = 48 cm²

Thus, the area is 48 cm².

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