Maths-
General
Easy
Question
Find the area of a triangle, two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
Hint:
Find third side using perimeter
The correct answer is: 69.65 cm2
Let third side be x
It is given that Perimeter of triangle = 42 cm
18 + 10 + x = 42
x = 42 – 28 = 14
So, length of third side is 14 cm
Using Heron’s formula,
Area of triangle =
where s = ![fraction numerator a plus b plus c over denominator 2 end fraction](data:image/png;base64,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)
s =
= 21
Area of triangle = ![square root of 21 left parenthesis 21 minus 18 right parenthesis left parenthesis 21 minus 14 right parenthesis left parenthesis 21 minus 10 right parenthesis end root](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAO0AAAATCAYAAAB81YrmAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA5JJREFUeNrtW01oE0EUXoqEUIooCCIKFSkiRUJBBUv10EvxICJSweBRKUVK8Sio4EUsIigVBNHiQfQg9ecgKEgoUqTEg4qHXEQ8eCiloFCKhhCN3+ALhsns7Jt0dmNm54OPJpOXvHnf7sy8NzsNAj56wJqnp2fbycYJcC7w8PDoGLwATyfk6ww4lRJdpyher4XXwkSLSGwCv9PfuJEDF1I2Ib6huL0WXguOFiyMg08V7UPgLLgCVsAP4EnN7+wEL5KdrqMDMfuwBY6vbnAaXAXL4Etwq2SzB5xPgRaNOBxSn6VFi/XgLbBIvE1tHC1YELXsqKL9NZinTSqBfhI3H/I798ExTTE9QN+P04dNcHzNgJfBdWCG0p6iwm6eLpLLWtQh+l/S2KZBiwJ4RJrECgwtWNgOLoNZpn0v+DHCJiyYq+BEzD7igM5XWXrfRSuDjEmpXnNRizrEqnJKY+u6Fscp+5JxQzHpTLZSx58D7xh+p9xiMCJ1PBizj6Rv1NWG1aA+aL8q7AalmdZFLeppbSHC1nUtRFo/omgfps90WrDwHjxkYD+oSGW4waxQChmnj6Rv1GmaLRv7fk1hl6H4XdYiQythb4St61p8C4lHtC1FaNFUZ8jYDS5SPcZBluq1oRaDqSbgI+kbNUfpcIXqsEXNqlFxXIspKc3V2bqsRZUZd2hbH3iPHByQPrsCXmd2cCP4LGTZtzVobfiQbWycPqlpaqwH4JaGmVVsKnwO1Fv5FYe1yClWQVuDttO0qBqm902D9gINWvEc9q302RdwL6NzO0i0vjUGo0uDbPlIckZ9EjI4Re0yt4aUsBO1KCr6ayM97kQtlkLiyZqmx+L0xW9wM73fD35ipMa7aKOq20Iwr0LSG5s+krw4ZYMZVd5wcE0Lk5XLdS1mQ/aJRlrZiPoBPqTXN8FLEZ0SA/yRQc0bFYxqa9+2jyQvTilkBein2rYRExS/q1qY2LquxbFA/URGZLz5CC2acBf8SUIs00ymw3OGjUkwqofotn0kfXFKlA53EYepph2XbDkHCjpZCxPbNGghyqOzwb9DN+eDvxuVUVo0YQP4C3wc8M55mhbqHLsFqQ6Mw4fNixLlSzxIf0ebCWW6MEclm7Djaq5pwbmp06KF2DyboXtCZLjiwEkPUwvlyK7RLNAO+IPhXguvhV6LJuyjQbutjZ0VqWNa/gVL1CtjXguvhaEWTRgNPDw8/kv8Aa7CmrDfM75lAAABCnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3FydD48bW4+MjE8L21uPjxtbz4oPC9tbz48bW4+MjE8L21uPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjE4PC9tbj48bW8+KTwvbW8+PG1vPig8L21vPjxtbj4yMTwvbW4+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTQ8L21uPjxtbz4pPC9tbz48bW8+KDwvbW8+PG1uPjIxPC9tbj48bW8+JiN4MjIxMjs8L21vPjxtbj4xMDwvbW4+PG1vPik8L21vPjwvbXNxcnQ+PC9tYXRoPrF/giUAAAAASUVORK5CYII=)
= ![square root of 21 left parenthesis 3 right parenthesis left parenthesis 7 right parenthesis left parenthesis 11 right parenthesis end root equals square root of left parenthesis 3 right parenthesis left parenthesis 7 right parenthesis left parenthesis 3 right parenthesis left parenthesis 7 right parenthesis left parenthesis 11 right parenthesis end root](data:image/png;base64,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)
= 21
cm2
(
= 3.31)
= 69.65 cm2
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