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Asked by Damanpreet Last Modified
Answer Let a be the third side.
∴ a + 12cm + 12cm = 30cm
⇒ a + 24cm = 30cm
∴ a = 30cm - 24cm = 6cm.
∴ the area of the triangle
= √ 15 ( 15 - 12 ) ( 15 - 12 ) ( 15 - 6 )
= √ 15 × 3 × 3 × 9 = √ 15 × 3 × 3 × 3 × 3
= 9 √15cm².
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Triangle ABC is an isosceles triangle with two equal sides
AB= 12 cm, AC= 12 cm, BC = x cm
perimeter of an triangle= sum of three sides
since it is an isosceles triangle, so in this case
30= 12+12+x
⇒x= 6cm
so the length of the side BC is 6 cm.
so in this way we find out the the length of all sides of triangle ABC, where AB= 12 cm, AC= 12 cm, and BC= 6 cm. Now draw a perpinduclar from point A in the line BC, let the middle point is P so in this way the length of BP and BC= 3 cm.
Now according to the pythagorus theorm we will find the length of AP
AB²= AP²+BP²
⇒144= AP²+9
⇒ AP= √135
so now area of triangle ABP= 1/2∗base*height
=1/2*3* √135
=3√135/2
so area of triangle ABC= 2* area of triangle ABP
= 2* 3√135/2
= 3√135
= 3*11.61
= 34.83 cm²
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The third side of the triangle will be 30-(12+12)cm
= 30-24 = 6cm.
Therefore the area of the triangle
= √S(s-a)(s-b)(s-c)
√15(15-12)(15-12)(15-6)
√15×3×3×9
9√15cm²
Answer : Area of the triangle is 9√15cm²
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Gautam Pal
Maths Teacher for classes 6th to 10th with 6 years experience and having my own YouTube Channel for clearing doubts
The perimeter of the isosceles triangle is the sum of all its three sides. Each of the equal sides is 12cm.
So, the third side of that isosceles triangle is = 30cm - (12cm + 12cm) = 30cm - 24cm = 6cm.
The area of that isosceles triangle, using Heron's Formula is, √15 (15-12) (15-12) (15-6) = √15x3x3x9 = 3x3x√15 = 9√15cm²
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Related Questions
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
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