ncert solutions class-9 maths chapter-12 exercise-12. · sol. since, the lengths of the sides of a...
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Q.1: The lengths of two sides of a triangle ABC are 10cm and 7cm and its perimeter is 28cm. Find the area of atriangle ABC.
Sol.
Given perimeter = 28cm
perimete:r Therefore, s = 2 = 14cm
And a= 10cm, b =?cm and c = 11cm (Since, perimeter= a+ b + c)
On applying Heron's Formula;
Area of Triangle ABC= Js(s - a)(s - b)(s - c)
Therefore, area of Triangle ABC
=J14(14 - 10)(14 - 7)(14 - 11)
(or) =✓14 x 4 x 7 x 3
= 14\1'6
Therefore, area of triangle ABC = 14\1'6cm2
Q.2: If perimeter of a triangular plot is 250m and the lengths of the sides of a triangular p lot are in the ratio of 4 : 7: 9. Find its area.
Sol.
Since, the lengths of the sides of a triangular plot are in the ratio of 4 : 7 : 9
Therefore, sides of triangular plot will be 4x, 7x and 9x
A
7x
B 9x
Given perimeter = 250m
Therefore, 4x + 7x + 9x = 250
Hence x = 12.5, that gives:
4x
C
a= 4x = 50m, b = 7x = 87.5m and c = 9x = 112.5m
And s = perimeter = 125m2
Now on applying Heron's Formula;
Area of plot ABC= Js(s - a)(s - b)(s - c)
NCERT SOLUTIONS CLASS-9 MATHS CHAPTER-12 EXERCISE-12.2
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