Question

4. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.​

Answer 1

Given :-

A  triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm,

To Find :-

Height of parallelogram

Solution :-

We know that

${\pmb{\red{\underline{Semi\;perimeter=\dfrac{a+b+c}{2}}}}}$

$\sf :\implies Semi-perimeter = \dfrac{26+28+30}{2}$

$\sf :\implies Semi-perimeter =\dfrac{84}{2}$

$\sf :\implies Semi-perimeter = 42\;cm$

Now,

${\pmb{\red{\underline{Area=\sqrt{s(s-a)(s-b)(s-c)}}}}$

$\sf :\implies Area = \sqrt{42(42-26)(42-28)(42-30)}$

$\sf :\implies Area = \sqrt{42\times 16\times 14\times 12}$

$\sf :\implies Area = \sqrt{1,12,896}$

$\sf :\implies Area = 336\;cm^2$

Now,

${\boxed{\frak{\red{Area \;of\;Triangle=Area\;of\;Parallelogram}}}}$

Let us assume that the height is h

$\sf :\implies 336=28\times h$

$\sf :\implies \dfrac{336}{28}=h$

$\sf :\implies 12=h$

${\textsf{\textbf{\underline{Hence, the height of paralleogram is 12 cm.}}}}$

Answer 2

Answer:

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Hope it's helpful!

Step-by-step explanation:

Given: Area of the parallelogram = Area of the triangle

By using the area of the parallelogram formula, we can calculate the height of the parallelogram

By using Heron’s formula, we can calculate the area of a triangle.

Heron's formula for the area of a triangle is: Area = √s(s - a)(s - b)(s - c)

Where a, b, and c are the sides of the triangle, and s = Semi-perimeter = Half the Perimeter of the triangle

Let ABCD is a parallelogram and ABE is a triangle having a common base with parallelogram ABCD.

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm, and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram

For ∆ABE, a = 30 cm, b = 26 cm, c = 28 cm

Semi Perimeter: (s) = Perimeter/2

s = (a + b + c)/2

= (30 + 26 + 28)/2

= 84/2

= 42 cm

By using Heron’s formula,

Area of a ΔABE = √s(s - a)(s - b)(s - c)

= √42(42 - 30)(42 - 28)(42 - 26)

= √42 × 12 × 14 × 16

= 336 cm2

Area of parallelogram ABCD = Area of ΔABE (given)

Base × Height = 336 cm2

28 cm × Height = 336 cm2

On rearranging, we get

Height = 336/28 cm = 12 cm

Thus, height of the parallelogram is 12 cm