Question

the base and height of the triangle are in the ratio 1 by 2 is to 1 by 5 and its area is 125 m square find its base and height​

Answer 1

Given

• The base and height of the triangle are in the ratio $\dfrac{1}{2}$ : $\dfrac{1}{5}$
• Area of the triangle = 125 m²

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To Find

• The base of the triangle
• The height of the triangle

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Solution

Let the base be $\dfrac{1}{2}x$ and the height be  $\dfrac{1}{5}x$ since they are in the ratio of $\dfrac{1}{2}$ : $\dfrac{1}{5}$.

Area of triangle = $\dfrac{1}{2}bh$

Here,

• b = Base
• h = Height

Apply the formula to find the value of 'x'.

⇒ $125 = \dfrac{1}{2}\times \dfrac{1}{2}x \times \dfrac{1}{5}x$

⇒ $125 = \dfrac{1}{20}x^{2}$

⇒ x² = 125 × 20

⇒ x² = 2500

⇒ x = √2500

⇒ x = 50 m

∴ The value of 'x' is 50 meters.

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Apply the value of 'x' to find the base and height of the triangle.

Base of Triangle

[tex]\implies \dfrac{1}{2}x \\ \\ \implies \dfrac{1}{2}\times 50 \\ \\ \bf \implies 25 \ m [/tex]

∴ The base of the triangle is 25 meters.

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Height of Triangle

[tex]\implies \dfrac{1}{5}x\\\\ \implies \dfrac{1}{5} \times 50 \\\\ \bf \implies 10 \ m [/tex]

∴ The height of the triangle is 10 meters.

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Answer 2

QUESTION :-

the base and height of the triangle are in the ratio 1 / 2 is to 1 / 5 and its area is 125 m square find its base and height

GIVEN :-

the base and height of the triangle are in the ratio 1 / 2 is to 1 / 5

area is 125 m square

TO FIND :-

find its base and height = ?

SOLUTION :-

Let base = 1/2 x height = 1/5x

Area of traingle = 1/2 × b × h

125 = 1/2 × 1/2x × 1/5x

125 = x² / 20

x² = 125 × 20

x² = 2500

x = 50

base = 1/2 × 50 = 25 m

height = 1/5 × 50 = 10 m

ANSWER :-

B = 25 m , h = 10 m