Question

the base and the height of a triangle are in the ratio of 4:3 and its area is 150 cm square find the base and height​

Answer 1

Area of Triangle = 10 cm²

Height = 4x

Base = 3x

= Area of Triangle = 150 cm²

= $\frac{1}{2}$ x Base x Height = 150 cm²

=  $\frac{1}{2}$ x 3x x 4x = 150 cm²

= 12x = 150 cm² x 2

= x = $\frac{300}{12}$

= x = 25 cm

∴ Height = 4x = 4 x 25 = 100 cm

    Base = 3x = 3 x 25 = 75 cm

Answer 2

Let x be parts , then ,

• Base = 4x
• Height = 3x

then ,

$\sf \underline{ \underline { \sf formula}} : \boxed{ \bf Area \: \: of \: \triangle = \frac{1}{2} \times b \times h}$

Substituting values we get ,

$\sf 150 = \frac{1}{2} \times( 4x) \times 3x$

$\sf 150 = \frac{12 {x}^{2} }{2}$

$\sf 12 {x}^{2} = 300 \implies {x}^{2} = \frac{300}{12} = 25$

$\sf x = \sqrt{25} = 5cm$

then ,

• Base of the ∆ = 4(5) = 20cm
• Height of the ∆ = 3(5) = 15cm

More Information :

Formulas :

$\sf Area \: \: of \: \: right \: \: angled \: \triangle = \frac{1}{2} \times b \times h$

$\sf Area \: \: of \: \: equilateral \: \triangle = \frac{ \sqrt{3} }{4} \times {a}^{2}$

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