Question

Fig. 17.27
1. A triangle and a parallelogram have the same base and the same area. If the sides of
the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14
cm, find the height of the parallelogram.​

Answer 1

Answer:

sides of the triangle = 13cm ,14cm and 15cm

semi perimeter of triangle =a+b+c/2

=13+14+15/2

=42/2

= 21cm

Area of triangle by Heron's formula = √s(s-a)(s-b)(s-c)

=√21(21-13)(21-14)(21-15)

=√21(8)(7)(6)

=√7×3×2×2×2×7×3×2

= 7×3×2×2√1

= 84cm

given base of parelleogram = 14cm

Area of parallelogram = Area of triangle

base ×height. = 84cm

14×height. = 84 cm

height. = 84/14

height. = 6cm

* therefore, the height of the parallelogram is 6cm.

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