Question

The base and height of triangle are in the ratio 2:3.If the area of a triangle is 180 cm2,find its base and height.​

Answer 1

Step-by-step explanation:

Question:-

The base and height of triangle are in ratio 2:3. If the area of the triangle is 180cm²,find its base and height.

Answer:-

Given :-

• The given figure is a triangle.

• Base and height are in ratio of 2:3

• Area of the triangle is 180cm².

To find :-

Base and height of the triangle

Process :-

Let the base of the triangle be 2x and height of the triangle be 3x.

∴ As we all know the formula of area of triangle:-

$⇒Area = \frac{1}{2} \times base \times height$

Now, putting the values in the equation:-

$⇒Area = \frac{1}{2} \times base \times height \\ \\ ⇒180 = \frac{1}{2} × 2x × 3x \\ \\ ⇒180 = \frac{1}{2} × 6x² \\ \\ ⇒ \frac{1}{2} ×6x² = 180 \\ \\ ⇒6x² = 180 × 2 \\ \\ ⇒6x² = 360 \\ \\ ⇒x² = \frac{360}{6} \\ \\ ⇒x² = 60 \\ \\ ⇒x = \sqrt{60} \\ \\ ⇒x = 7.74$

∴ Substituting the values:-

⇒2x = 2× 7.74 = 15.48cm

⇒3x = 3 × 7.74 = 23.22cm

Required Answer:-

Base = 15.48cm

Height = 23.22cm

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Hope it helps you...

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