Question

a triangle and a rectangle have the same area . if the sidesbof the triangle are 13cm 14cm 15cm and rectangle standa on the side 14cm find the breath of the rectangle

Answer 1

$Hey\:There$
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Given that, Sides of ∆ are 13 cm, 14 cm and 15 cm. And length of rectangle is 14 cm.

By Heron's formula ;
s = ( A + B + C ) / 2
s = ( 13 + 14 + 15 ) / 2
s = 42 / 2
s = 21

Now, area of ∆ = √[s(s–A)(s–B)(s–C)]
= √[21(21–13)(21–14)(21–15)]
= √[21(8)(7)(6)]
= √7056
= 84 cm²

Since, area of ∆ = area of rectangle
84 cm² = L × B
84 cm² = 14 × B
B = 84 / 14
B = 6 cm.

Therefore, breadth of rectangle is 6 cm.
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$Hope\: my \: ans.'s \: satisfactory.$ (^-^)

Answer 2

You just have to find the area of the triangle and as it is equal to that of the triangle just equate the values . So it will look something like this :
Area of triangle by Heron’s formula = s(s-a)(s-b)(s-c) whole under root

S= 1/2 of perimeter
= 13+14+15/2
= 21

Area = under root 21(21-13)(21-14)(21-15)
= under root 21.8.7.6
= 84
Now equate it with sides
Area of rect. = l.b
84=14.b
b=84/14=6