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Area and Perimeter of Plane Figures — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSArea and Perimeter of Plane Figures5 Marks
Question
A triangle and a parallelogram have the same base and the same area. If the side of the triangle is $26 \sim \ cm, 28 \sim \ cm$, and $30 \sim \ cm$ and the parallelogram stands on the base $28 \sim \ cm$, find the height of the parallelogram.
✓

Answer

Let the sides of the triangle be
$a = 26 \ cm, b = 28 \ cm$ and $c = 30 \ cm$
Now,
semi$-$perimeter of a triangle,
$s =\frac{a+b+c}{2}=\frac{26+28+30}{2}=\frac{84}{2}=42 \ cm$
$\therefore$ Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{42 \times 16 \times 14 \times 12}$
$=\sqrt{7 \times 6 \times 4 \times 4 \times 7 \times 2 \times 6 \times 2}$
$=\sqrt{7 \times 7 \times 4 \times 4 \times 6 \times 6 \times 2 \times 2}$
$= 7 \times 4 \times 6 \times 2$
$= 336 \ cm^2$
Base of a parallelogram $= 28 \ cm$
Given ,
Area of parallelogram $=$ Area of triangle
$\Rightarrow $ Base $\times $Height $= 336$
$\Rightarrow 28 \times$ Height $= 336$
$\Rightarrow $ Height $= 12 \ cm$

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