Question

Base of a triangle is 15 and height is 6. Base of another triangle is 12 and height is 5. Then the ratio of the areas of these triangles are __________.​

Answer 1

Answer -

• The ratio of the area of the two triangles = 3 : 2.

To find -

• The ratio of the area of the two triangles.

Step-by-step explanation -

• Here, the base and height of two triangles are given to us. We have to find the ratio of their areas.

Used formula -

$\bigstar \: \underline{\boxed{\sf Area_{(triangle)} = \dfrac{1}{2} \times Base \times Height}}$

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Finding the area of the first triangle -

• Here, the base of the triangle = 15 units and it's height = 6 units.

$\longrightarrow \: \dfrac{1}{2} \times 15 \times 6$

$\longrightarrow \: \dfrac{1}{2} \times 90$

$\longrightarrow \: \cancel{\dfrac{90}{2}}$

$\rm \longrightarrow \: 45 \: sq.units$

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Finding the area of the second triangle -

• Here, the base of the triangle = 12 units and it's height = 5 units.

$\longrightarrow \: \dfrac{1}{2} \times 12 \times 5$

$\longrightarrow \: \dfrac{1}{2} \times 60$

$\longrightarrow \: \cancel{\dfrac{60}{2}}$

$\rm \longrightarrow \: 30 \: sq.units$

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Finding the ratio of the area of the two triangles -

$\bf \longmapsto \cancel{\dfrac{45}{30}}$

$\bf \longmapsto \dfrac{3}{2}$

$\bf\longmapsto 3 : 2$

Hence -

• The ratio of the areas of these two triangles = 3 : 2.

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Answer 2

Question :-

Base of a triangle is 15 and height is 6. Base of another triangle is 12 and height is 5. Then the ratio of the areas of these triangles are __________.

Solution :-

Given :

By first triangle,

• Base = 15
• Height = 6

By second triangle,

• Base = 12
• Height = 5

Need to find :

• Ratio of both triangle

Required Formula :

${\boxed{\rm{\red{Area \: of \: triangle = \frac{1}{2} × base × height}}}}$

Area of first triangle

$\sf:\longmapsto{A= \frac{1}{2} \times 15 \times 6 } \\ \\ \sf:\longmapsto{A= \frac{1}{2} \times 90 } \: \: \: \: \: \\ \\ \sf:\longmapsto{A=45} \: \: \: \: \: \: \: \: \: \: \: \:$

Area of first triangle is 45.

Area of second triangle

$\sf:\longmapsto{A= \frac{1}{2} \times 12 \times 5} \\ \\ \sf:\longmapsto{A= \frac{1}{2} \times 60} \: \: \: \: \: \: \\ \\ \sf:\longmapsto{A=30} \: \: \: \: \: \: \: \: \: \: \: \: \:$

Area of second triangle is 30.

Ratio of both triangle

$\sf:\longmapsto{ \cancel \frac{45}{30} } \: \: \: \\ \\ \sf:\longmapsto{ \frac{3}{2} } \: \: \: \: \: \\ \\ \sf:\longmapsto{3 :2 }$

The ratio of both triangle is 3:2.

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