Question

1
20. Base of a triangle is 9 and
height is 5. Base of another triangle
is 10 and height is 6. Find the ratio
of areas of these triangles. *
O 45: 60
60:45
O 9:10
O 5:6​

Answer 1

Answer :

The ratio of areas of these triangles is 45:60.

Given :

• Base of 1st triangle is 9 units and height is 5 units.
• Base of 2nd triangle is 10 units and height is 6 units.

To find :

• Ratio of areas of these triangles.

Solution :

Formula used :-

${\boxed{\sf{Area\:of\: triangle=\dfrac{1}{2}\times\:base\times\: height}}}$

★ In case of 1st triangle ,

• Base = 9 units
• Height = 5 units

Then,

$\sf{Area\:of\:1st\: triangle=\dfrac{1}{2}\times\:9\times\:5\: units^2}$

$\to\sf{Area\:of\:1st\: triangle=\dfrac{45}{2}\: units^2}$

★ In case of 2nd triangle ,

• Base = 10 units
• Height = 6 units

Then,

$\sf{Area\:of\:2nd\: triangle=\dfrac{1}{2}\times\:10\times\:6\: units^2}$

$\to\sf{Area\:of\:2nd\: triangle=10\times\:30\: units^2}$

$\to\sf{Area\:of\:2nd\: triangle=30\: units^2}$

Ratio of these 2 triangles ,

= $\sf{\dfrac{45}{2}:30}$

= $\sf{\dfrac{\dfrac{45}{2}}{30}}$

= $\sf{\dfrac{45}{2\times\:30}}$

= $\sf{\dfrac{45}{60}}$

= 45 : 60

• Ratio of areas of these 2 triangles = 45:60.

Answer 2

GIVEN :-

• Base and height of first triangle = 9and 5 units
• base and height of another Triangle = 10 and 6 units

TO FIND :-

• The ratio of both the triangles.

SOLUTION :-

$\to \: \rm \: \dfrac{Area \: (1 \triangle)}{Area \: (2 \triangle)} \\ \\ \to \rm \:\dfrac{ \bigg( \dfrac{1}{2} \times base \: \times height \bigg) }{ \bigg(\dfrac{1}{2} \times base \: \times height \bigg)} \\ \\ \to \rm \: \dfrac{ \bigg(\dfrac{1}{2} \times 9 \times 5 \bigg)}{ \bigg(\dfrac{1}{2} \times 10 \times 6 \bigg)} \\ \\ \to \rm \: \bigg(\dfrac{ \dfrac{45}{2} }{30} \bigg ) \\ \\ \to \rm \: \dfrac{45}{2} \times \dfrac{1}{30} \\ \\ \to \rm \: \dfrac{45}{60} \\ \\ \to \boxed{ \red{ \bf \:\dfrac{Area \: (1 \triangle)}{Area \: (2 \triangle)} \: = 45\ratio \: 60}}$

Hence the ratio of both the triangle is 45:60

Hence option (a) is correct ✔

EXTRA INFORMATION :-

◉ Some formulae of triangle,

$\implies \bf \: Area (\triangle) = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \implies \bf \: semi \: perimeter (\triangle) = \dfrac{a \: + b \: + c}{2} \\ \\ \implies \bf \: perimeter (\triangle) = a \: + \: b \: + \: c$