Question

7. The area of a triangle is the same as that of a rectangle. If the length and he
breadth of the rectangle are 24 cm and 18 cm respectively and the base of the
triangle is 12 cm, find the height of the triangle.​

Answer 1

Given :

• Area of triangle is the same as that of a rectangle.
• Length and Breadth of the rectangle are 24 cm and 18 cm respectively .
• Base of Triangle is 12 cm .

To Find :

• Height of Triangle .

Solution :

Firstly we will find Area of Rectangle :

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Rectangle=l\times{b}}$

Putting Values :

$\longmapsto\tt{24\times{18}}$

$\longmapsto\tt\bf{432\:{cm}^{2}}$

Now ,

As Given that area of triangle is the same as that of a rectangle. So ,

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:\triangle=\dfrac{1}{2}\times{b}\times{h}}$

Putting Values :

$\longmapsto\tt{432=\dfrac{1}{{\cancel{2}}}\times{{\cancel{12}}}\times{h}}$

$\longmapsto\tt{432=6\times{h}}$

$\longmapsto\tt{\cancel\dfrac{432}{6}=h}$

$\longmapsto\tt\bf{72\:cm=h}$

So , The Height of Triangle is 72 cm .

Answer 2

$\rm{ \underline{ \huge{ \purple{Given: }}}}$

• Length of rectangle = 24 cm
• Breadth of rectangle = 18 cm
• Base of triangle = 12 cm
• Area of rectangle = Area of triangle

$\rm{ \underline{ \huge{ \purple{ To \: find: }}}}$

• Height of the triangle

$\rm{ \underline{ \huge{ \purple{ Solution: }}}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\ \mathfrak{ \underline{Formula \: to \: calculate \: area \: of \: rectangle}}$

$\boxed {\large{ \mathfrak{ \red{ area = length \times breadth}}}}$

According to question,

$\large{ \sf : \implies \: \: \: \: \: \: \: \: \: \: \: area = 24 \times 18}$

$\large{ \sf : \implies \: \: \: \: \: \: \: \: \: \: \: area = 432 \: {cm}^{2} }$

• Area of rectangle is 432 cm²

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\ \mathfrak{ \underline{Formula \: to \: calculate \: area \: of \: triangle}}$

$\boxed {\large{ \mathfrak{ \red{ area = \frac{1}{2} \times base \times height}}}}$

According to question,

$\large{ \tt : \implies \: \: \: \: \: \: \: \: \: \: \: \frac{1}{2} \times 12 \times h = 432}$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: \: \: \: 12 \times h = 432 \times 2}$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: \: \: \: h = \frac{432 \times 2}{12} }$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: \: \: \: h = 72}$

$\rm{ \underline{ \huge{ \purple{ Hence:}}}}$

• The height of triangle is 72 cm