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The area of a parallelogram with a base 24cm is equal to the area of a triangle

of sides 10cm, 24m and 26cm. Find the altitude of the parallelogram.

Class: Grade 9

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6 cm

3 cm

5 cm

8 cm

answer is C.

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Detailed Solution

Let the height of the parallelogram beh. Area of parallelogram = base

\times

height
= 24

\times

h
= 24h
Semi-perimeter of triangle with sides10 cm,24 cm and 26 cm is
s=

\frac{a + b + c}{2}

\frac{10 + 24 + 26}{2}

=2 60
= 30cm
How by using heron's formula, Area of triangle
=

\sqrt{330130 - 40) (30 - 24] (30 - 26)}

\sqrt{3 56 \times 5 \times 5 \times 4 \times 4 \times 6}

= 120 sq.cm
But it is given that area of the parallelogram is equal to the area of triangle
24h = 120
h=

\frac{120}{24}

h=5 cm

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